Systems and methods for achieving orthogonal control of non-orthogonal qubit parameters

ABSTRACT

Achieving orthogonal control of non-orthogonal qubit parameters of a logical qubit allows for increasing the length of a qubit chain thereby increasing the effective connectivity of the qubit chain. A hybrid qubit is formed by communicatively coupling a dedicated second qubit to a first qubit. By tuning a programmable parameter of the second qubit of a hybrid qubit, an effective programmable parameter of the hybrid qubit is adjusted without affecting another effective programmable parameter of the hybrid qubit thereby achieving orthogonal control of otherwise non-orthogonal qubit parameters. The length of the logical qubit may thus be increased by communicatively coupling a plurality of such hybrid qubits together.

BACKGROUND Field

This disclosure generally relates to controlling the parameters ofqubits in a quantum processor.

Quantum Devices

Quantum devices are structures in which quantum mechanical effects areobservable. Quantum devices include circuits in which current transportis dominated by quantum mechanical effects. Such devices includespintronics, where electronic spin is used as a resource, andsuperconducting circuits. Both spin and superconductivity are quantummechanical phenomena. Quantum devices can be used for measurementinstruments, in computing machinery, and the like.

Quantum Computation

Quantum computation and quantum information processing are active areasof research and define classes of vendible products. A quantum computeris a system that makes direct use of quantum-mechanical phenomena, suchas, superposition, tunneling, and entanglement, to perform operations ondata. The elements of a quantum computer are not binary digits (bits)but typically are quantum binary digits or qubits. Quantum computershold the promise of providing exponential speedup for certain classes ofcomputation problems like simulating quantum physics. Useful speedup mayexist for other classes of problems.

There are several types of quantum computers. An early proposal fromFeynman in 1981 included creating artificial lattices of spins. Morecomplicated proposals followed including a quantum circuit model wherelogical gates are applied to qubits in a time ordered way. In 2000, amodel of computing was introduced for solving satisfiability problems;based on the adiabatic theorem this model is called adiabatic quantumcomputing. This model is believed useful for solving hard optimizationproblems and potentially other problems.

Adiabatic Quantum Computation

Adiabatic quantum computation typically involves evolving a system froma known initial Hamiltonian (the Hamiltonian being an operator whoseeigenvalues are the allowed energies of the system) to a finalHamiltonian by gradually changing the Hamiltonian. A simple example ofan adiabatic evolution is a linear interpolation between an initialHamiltonian and a final Hamiltonian. An example is given by:H _(e)=(1−s)H _(i) +sH _(f)  (1)where H_(i) is the initial Hamiltonian, H_(f) is the final Hamiltonian,H_(e) is the evolution or instantaneous Hamiltonian, and s is anevolution coefficient which controls the rate of evolution. As thesystem evolves, the evolution coefficient s goes from 0 to 1 such thatat the beginning (i.e., s=0) the evolution Hamiltonian H_(e) is equal tothe initial Hamiltonian H_(i) and at the end (i.e., s=1) the evolutionHamiltonian H_(e) is equal to the final Hamiltonian H_(f). Before theevolution begins, the system is typically initialized in a ground stateof the initial Hamiltonian H_(i) and the goal is to evolve the system insuch a way that the system ends up in a ground state of the finalHamiltonian H_(f) at the end of the evolution. If the evolution is toofast, then the system can be excited to a higher energy state, such asthe first excited state. In the present systems and devices, an“adiabatic” evolution is an evolution that satisfies the adiabaticcondition:{dot over (s)}|

1|dH _(e) /ds|0

|=δg ²(s)  (2)where {dot over (s)} is the time derivative of s, g(s) is the differencein energy between the ground state and first excited state of the system(also referred to herein as the “gap size”) as a function of s, and δ isa coefficient much less than 1. Generally the initial Hamiltonian H_(i)and the final Hamiltonian H_(f) don't commute. That is, [H_(i),H_(f)]≠0.

The process of changing the Hamiltonian in adiabatic quantum computingmay be referred to as evolution. The rate of change, for example, changeof s, is slow enough that the system is always in the instantaneousground state of the evolution Hamiltonian during the evolution, andtransitions at anti-crossings (i.e., when the gap size is smallest) areavoided. The example of a linear evolution schedule is given above.Other evolution schedules are possible including non-linear, parametric,and the like. Further details on adiabatic quantum computing systems,methods, and apparatus are described in, for example, U.S. Pat. Nos.7,135,701 and 7,418,283.

Quantum Annealing

Quantum annealing is a computation method that may be used to find alow-energy state, typically preferably the ground state, of a system.Similar in concept to classical annealing, the method relies on theunderlying principle that natural systems tend towards lower energystates because lower energy states are more stable. However, whileclassical annealing uses classical thermal fluctuations to guide asystem to a low-energy state and ideally its global energy minimum,quantum annealing may use quantum effects, such as quantum tunneling, toreach a global energy minimum more accurately and/or more quickly thanclassical annealing. In quantum annealing thermal effects and othernoise may be present to aid the annealing. However, the final low-energystate may not be the global energy minimum. Adiabatic quantumcomputation, therefore, may be considered a special case of quantumannealing for which the system, ideally, begins and remains in itsground state throughout an adiabatic evolution. Thus, those of skill inthe art will appreciate that quantum annealing systems and methods maygenerally be implemented on an adiabatic quantum computer. Throughoutthis specification and the appended claims, any reference to quantumannealing is intended to encompass adiabatic quantum computation unlessthe context requires otherwise.

Quantum annealing uses quantum mechanics as a source of disorder duringthe annealing process. The optimization problem is encoded in aHamiltonian H_(P), and the algorithm introduces quantum effects byadding a disordering Hamiltonian H_(D) that does not commute with H_(P).An example case is:H _(E) ∝A(t)H _(D) +B(t)H _(P)  (3)where A(t) and B(t) are time dependent envelope functions. TheHamiltonian H_(E) may be thought of as an evolution Hamiltonian similarto H_(e) described in the context of adiabatic quantum computationabove. The disorder may be removed by removing H_(D) (i.e., reducingA(t)). The disorder may be added and then removed. Thus, quantumannealing is similar to adiabatic quantum computation in that the systemstarts with an initial Hamiltonian and evolves through an evolutionHamiltonian to a final “problem” Hamiltonian H_(P) whose ground stateencodes a solution to the problem. If the evolution is slow enough, thesystem will typically settle in the global minimum (i.e., the exactsolution), or in a local minimum close in energy to the exact solution.The performance of the computation may be assessed via the residualenergy (difference from exact solution using the objective function)versus evolution time. The computation time is the time required togenerate a residual energy below some acceptable threshold value. Inquantum annealing, H_(P) may encode an optimization problem but thesystem does not necessarily stay in the ground state at all times. Theenergy landscape of H_(P) may be crafted so that its global minimum isthe answer to the problem to be solved, and low-lying local minima aregood approximations.

The reduction of the envelope function A(t) in quantum annealing mayfollow a defined schedule known as an annealing schedule. This is anexample of an evolution schedule. Unlike traditional forms of adiabaticquantum computation where the system begins and remains in its groundstate throughout the evolution, in quantum annealing the system may notremain in its ground state throughout the entire annealing schedule. Aswell, quantum annealing may be implemented as a heuristic technique,where low-energy states with energy near that of the ground state mayprovide approximate solutions to the problem.

Superconducting Qubits

There is a type of solid state qubit which is based on circuits ofsuperconducting materials. Superconducting material conducts withoutelectrical resistance under certain conditions like below a criticaltemperature, a critical current, or a magnetic field strength, or forsome materials above a certain pressure. There are two superconductingeffects that underlie how superconducting qubits operate: fluxquantization, and Josephson tunneling.

Flux is quantized when a loop of superconducting material, threaded by amagnetic flux, is cooled below its superconducting critical temperaturewhile the field is switched off. The supercurrent continues in an effortto maintain the flux. The flux is quantized. Thus, superconductivity isnot simply the absence of electrical resistance but rather a quantummechanical effect. All the current in the loop is governed by a singlewavefunction and for the wavefunction to be single valued at any pointin the loop the flux is quantized.

Josephson tunneling is where the current tunnels through a minorinterruption in the loop, such as an insulating gap of a few nanometers.The amount of current is sinusoidally dependent on the phase differenceacross the interruption. This sinusoidally dependency is a non-linearitythat leads to an harmonicity in the energy levels of the system.

These superconducting effects present in different configurations togive rise to different types of superconducting qubits including flux,phase, charge, and charge-phase qubits. Charge-phase qubits are alsoknown as hybrid qubits. These different types of qubits depend on thetopology of the loops and the physical parameters of the parts of theloops, such as, inductance, capacitance, and persistent current.

Persistent Current

A superconducting flux qubit may comprise a loop of superconductingmaterial (called a “qubit loop”) that is interrupted by at least oneJosephson junction. Since the qubit loop is superconducting, iteffectively has no electrical resistance. Thus, electrical currenttraveling in the qubit loop may experience no dissipation. If anelectrical current is coupled into the qubit loop by, for example, amagnetic flux signal, this current may continue to circulate around thequbit loop even when the signal source is removed. The current maypersist indefinitely until it is interfered with in some way or untilthe qubit loop is no longer superconducting (due to, for example,heating the qubit loop above its critical temperature). For the purposesof this specification, the term “persistent current” is used to describean electrical current circulating in superconducting loop interrupted byat least one Josephson junction. The sign and magnitude of a persistentcurrent may be influenced by a variety of factors, including but notlimited to a flux signal ϕ_(X) coupled directly into the superconductingloop and a flux signal ϕ_(CJJ) (or ϕ_(co)) coupled into a compoundJosephson junction that interrupts the superconducting loop.

Quantum Processor

A quantum processor may take the form of a superconducting quantumprocessor. A superconducting quantum processor may include a number ofqubits and associated local bias devices, for instance two or moresuperconducting qubits. A superconducting quantum processor may alsoemploy coupling devices (i.e., “couplers”) providing communicativecoupling between qubits. A qubit and a coupler resemble each other butdiffer in physical parameters. One difference is the screeningparameter, β. Consider an rf-SQUID, superconducting loop interrupted bya Josephson junction, β is the ratio of the inductance of the Josephsonjunction to the geometrical inductance of the loop. A design with lowervalues of β, about 1, behaves more like a simple inductive loop, amonostable device. A design with higher values is more dominated by theJosephson junctions, and is more likely to have bistable behavior. Theparameter, β is defined a 2πLI_(C)/Φ₀. That is, β is proportional to theproduct of inductance and critical current. One can vary the inductance,for example, a qubit is normally larger than its associated coupler. Thelarger device has a larger inductance and thus the qubit is often abistable device and a coupler monostable. Alternatively the criticalcurrent can be varied, or the product of the critical current andinductance can be varied. A qubit often will have more devicesassociated with it. Further details and examples quantum processors thatmay be used in conjunction with the present systems and devices aredescribed in, for example, U.S. Pat. Nos. 7,533,068; 8,008,942;8,195,596; 8,190,548; and 8,421,053.

The types of problems that may be solved by any particular embodiment ofa quantum processor, as well as the relative size and complexity of suchproblems, typically depend on many factors. Two such factors may includethe number of qubits in the quantum processor and the connectivity(i.e., the availability of communicative couplings) between the qubitsin the quantum processor. Throughout this specification, the term“connectivity” is used to describe the maximum number of possiblecommunicative coupling paths that are physically available (e.g.,whether active or not) to communicably couple between individual qubitsin a quantum processor without the use of intervening qubits. Forexample, a qubit with a connectivity of three is capable of communicablycoupling to up to three other qubits without any intervening qubits. Inother words, there are communicative coupling paths available to threeother qubits, although in any particular application all or less thanall (e.g., zero, one, two, or three) of those communicative couplingpaths may be employed. In a quantum processor employing coupling devicesbetween qubits, this would mean a qubit having a connectivity of threeis selectively communicably coupleable to each of three other qubits viaa respective one of three coupling devices. Typically, the number ofqubits in a quantum processor limits the size of problems that may besolved and the connectivity between the qubits in a quantum processorlimits the complexity of the problems that may be solved.

Many prior art techniques for using adiabatic quantum computation and/orquantum annealing to solve computational problems involve finding waysto directly map/embed a representation of a problem to the quantumprocessor itself. For example, US Patent Publication 2008-0052055describes solving a protein folding problem by first casting the proteinfolding problem as an Ising spin glass problem and then embedding theIsing spin glass problem to a quantum processor, and U.S. Pat. No.8,073,808 describes solving a computational problem (e.g., animage-matching problem) by first casting the problem as a quadraticunconstrained binary optimization (“QUBO”) problem and then embeddingthe QUBO problem directly on a quantum processor. In both cases, aproblem is solved by first casting the problem in a contrivedformulation (e.g., Ising spin glass, QUBO, etc.) because that particularformulation maps directly to the particular embodiment of the quantumprocessor being employed. In other words, an intermediate formulation isused to re-cast the original problem into a form that accommodates thenumber of qubits and/or connectivity constraints in the particularquantum processor and then the intermediate formulation is embedded onthe quantum processor. This “embedding” approach is motivated bylimitations inherent in the architecture of the quantum processor beingemployed. For example, a quantum processor that employs only pair-wiseinteractions between qubits (i.e., a quantum processor employingcoupling devices that provide communicative coupling between respectivepairs of qubits but not, for example, between larger sets of qubits,such as three or more qubits) is intrinsically well-suited to solveproblems having quadratic terms (e.g., QUBO problems) because quadraticterms in a problem map directly to pair-wise interactions between qubitsin the quantum processor.

Qubit Chains

The approach of re-casting a problem in an intermediate formulation andthen embedding the intermediate formulation to the quantum processorcommonly employs qubit chains comprising multiple superconducting qubitscoupled together to behave as a single logical qubit. Techniques forforming logical qubits as qubit chains are described in, for example,U.S. Pat. Nos. 7,984,012, 8,244,662, and 8,174,305. Each individualqubit within a chain of qubits may have individual qubit parameters suchas tunneling amplitude and persistent current. The chain itself may have“effective” qubit parameters such as effective tunneling amplitude andeffective persistent current, where the effective qubit parameters ofthe chain are influenced by the individual qubit parameters of theindividual qubits that make up the chain. For example, the effectivetunneling amplitude of a chain of qubits may be related to the sum ofthe individual tunneling amplitudes of the individual qubits that makeup the chain. Similarly, each of the qubits that make up a chain mayhave an individual connectivity, while the complete chain may have aneffective connectivity that is related to the sum of the individualconnectivities of the individual qubits that make up the chain. A chainof qubits when represented as a logical qubit represents a singlevariable of a problem. A chain of qubits may not necessarily always be alogical qubit. Individual qubits in a chain of qubits may representdifferent variables or the individual qubits in the chain of qubits maytogether represent a single variable. When a chain of qubitscollectively behaves as a single qubit thereby representing a singlevariable of a problem, the chain of qubit may also be referred to as a“logical qubit.”

When embedding a problem in a quantum processor, a single variable ofthe problem may be mapped to a chain of individual qubits. Increasingthe number of qubits in a qubit chain increases the effectiveconnectivity of the variable that is mapped to that chain, and thereforefacilitates long-range pair-wise coupling between variables. Inpractice, however, there are limitations to the number of qubits thatcan be coupled together to form a single logical qubit. The effectivetunneling amplitude of a qubit chain with N superconducting qubits,where each individual qubit has a tunneling amplitude of Δ_(i) and thechain comprises a total of N−1 couplings J_(i) between individual qubitsi, in the perturbative regime of Δ<<J, is:

$\begin{matrix}{\Delta_{eff}\text{∼}\frac{\prod\limits_{i = 1}^{N}\;\Delta_{i}}{\prod\limits_{i = 1}^{N - 1}\; J_{i}}} & (4)\end{matrix}$If all Δ_(i) and J_(i) are identical, then:

$\begin{matrix}{\Delta_{eff}\text{∼}{\Delta( \frac{\Delta}{J} )}^{N}} & (5)\end{matrix}$which is exponentially dependent on N. This makes a longer qubit chain(i.e., a chain having a larger N value) have a very small effectivetunneling amplitude for a large portion of the quantum annealing time,thereby making the qubits behave like classical bits with fixedorientations and impeding the quantum annealing process.

BRIEF SUMMARY

Increasing the length of a chain of qubits is desirable because suchincreases the effective connectivity of the qubit chain, allowing morecomplicated problems to be mapped to the quantum processor. Therefore,there is a need in the art for systems and/or methods of increasing thelength of a qubit chain in a quantum processor without degrading theeffective parameters (such as the effective tunneling amplitude) of thequbit chain.

Orthogonality of Qubit Parameters

The tunneling amplitude of a superconducting qubit can be adjusted bychanging the barrier height of the superconducting qubit. However,adjusting the tunneling amplitude of a qubit by changing the barrierheight affects the persistent current of the qubit which would changethe programmable parameters (such as the spin denoted by h, and couplingdenoted by J) assigned to the qubit in a given problem to be solved. Inother words, the tunneling amplitude and the persistent current of anindividual qubit are non-orthogonal qubit parameters. Therefore,adjusting the tunneling amplitude of a superconducting qubit in a chainof superconducting qubits not only changes the programmable parametersof that particular qubit, but also the programmable parameters of theother superconducting qubits in the qubit chain that are coupled to thatqubit. This sets a limit to the number of qubits that can be coupledtogether to behave as a single logical qubit. Therefore, there is a needin the art for techniques for achieving orthogonal control ofnon-orthogonal qubit parameters so that for example, adjusting thetunneling amplitude of a superconducting qubit would not affect thepersistent current of the superconducting qubit and as a result multiplequbits can be coupled together to form longer chains or sets ofsuperconducting qubits to increase the effective connectivity of thequantum processor.

A method of controlling qubit parameters in a quantum processor, whereinthe quantum processor includes a plurality of qubits, each qubit havinga respective first programmable parameter and a respective secondprogrammable parameter that at least partially depends on the respectivefirst programmable parameter, and a plurality of coupling devices thateach selectively provide communicative coupling between respective pairsof the qubits may be summarized as including communicatively coupling atleast three of the qubits to one another as a single logical qubit, thesingle logical qubit formed by a first outermost qubit, a secondoutermost qubit and at least one intermediary qubit, the at least oneintermediary qubit strongly communicatively coupled between the firstand the second outermost qubits, the first outmost qubit being anoutermost qubit of the qubits of the logical qubit in a first directionalong a logical qubit path defined by the qubits of the logical qubitand the second outermost qubit being an outermost qubit in a seconddirection along the logical qubit path; programming the first and thesecond outermost qubits to have respective first programmable parametersless than or equal to a first value; and programming the at least one ofthe intermediate qubits to have at least approximately near zero spinand to have respective values of the first programmable parameter higherthan the first value. Communicatively coupling at least three of thequbits to one another as a single logical qubit may includecommunicatively coupling at least two qubits as respective intermediatequbits communicatively coupled between the first and the secondoutermost qubits; and programming the at least one intermediate qubit tohave at least approximately near zero spin and to have respective valuesof the first programmable parameter higher than the first value includesprogramming all of the intermediate qubits to have at leastapproximately near zero spin and to have respective values of the firstprogrammable parameter higher than the first value. The firstprogrammable parameter may be tunneling amplitude, and programming thefirst programmable parameter of the first and the second outermostqubits may include programming a respective tunneling amplitude of thefirst and the second outermost qubits via a programming subsystem. Thesecond programmable parameter may be a persistent current of the secondqubit, and programming the tunneling amplitude of the at least one ofthe intermediate qubits may include programming a respective tunnelingamplitude of the at least one of the intermediate qubits via theprogramming subsystem without substantially affecting the persistentcurrent of the first and the second outermost qubits.

A quantum processor apparatus may be summarized as including a pluralityof qubits, each qubit having a respective first programmable parameterand a respective second programmable parameter that at least partiallydepends on the respective first programmable parameter, and a pluralityof coupling devices that each selectively provide communicative couplingbetween respective pairs of the qubits, wherein: at least three of thequbits are communicatively coupled to one another as a single logicalqubit, the single logical qubit formed by a first outermost qubit, asecond outermost qubit and at least one intermediary qubit, the at leastone intermediary qubit strongly communicatively coupled between thefirst and the second outermost qubits, the first outmost qubit being anoutermost qubit of the qubits of the logical qubit in a first directionalong a logical qubit path defined by the qubits of the logical qubitand the second outermost qubit being an outermost qubit in a seconddirection along the logical qubit path; the first and the secondoutermost qubits have respective first programmable parameters less thanor equal to a first value; and the at least one of the intermediatequbits to have at least approximately near zero spin and to haverespective values of the first programmable parameter higher than thefirst value. The single logical qubit may include at least two qubits asrespective intermediate qubits communicatively coupled between the firstand the second outermost qubits, and all of the intermediate qubits tohave at least approximately near zero spin and to have respective valuesof the first programmable parameter higher than the first value. Thefirst programmable parameter may be tunneling amplitude, and arespective tunneling amplitude of the first and the second outermostqubits may be less than or equal to the first value. The secondprogrammable parameter may be a persistent current of the second qubit,and a respective tunneling amplitude of the at least one of theintermediate qubits may not substantially affect the persistent currentof the first and the second outermost qubits.

The quantum processor may further include at least one first programmingsubsystem communicatively coupleable to a compound Josephson junction ofat least one of the qubits and operable to program a tunneling amplitudeof the at least one of the qubits; and at least one second programmingsubsystem communicatively coupleable to a qubit loop of at least one ofthe qubits and operable to program a persistent current of the at leastone of the qubits.

A method of controlling qubit parameters in a quantum processor, whereinthe quantum processor includes a plurality of qubits, each qubit havinga respective first programmable parameter and a respective secondprogrammable parameter that at least partially depends on the respectivefirst programmable parameter, and a plurality of coupling devices thateach selectively provide communicative coupling between respective pairsof the qubits may be summarized as including communicatively coupling atleast three of the qubits to one another as a single logical qubit, thesingle logical qubit formed by a first outermost qubit, a secondoutermost qubit and at least one intermediary qubit, the at least oneintermediary qubit strongly communicatively coupled between the firstand the second outermost qubits, the first outmost qubit being anoutermost qubit of the qubits of the logical qubit in a first directionalong a logical qubit path defined by the qubits of the logical qubitand the second outermost qubit being an outermost qubit in a seconddirection along the logical qubit path; for at least one of the at leastone intermediate qubits of the logical qubit, communicatively couplingan orthogonal control qubit to the respective intermediate qubit suchthat the orthogonal control qubit is not communicatively coupled to anyother qubit except via the respective intermediate qubit; programmingthe first and the second outermost qubits to have respective firstprogrammable parameters less than or equal to a first value; andprogramming the orthogonal control qubit to have a value of the firstprogrammable parameter higher than the first value. Communicativelycoupling at least three of the qubits to one another as a single logicalqubit may include communicatively coupling at least two qubits asrespective intermediate qubits communicatively coupled between the firstand the second outermost qubits; communicatively coupling a respectiveorthogonal control qubit to each of the respective intermediate qubits.Communicatively coupling at least three of the qubits to one another asa single logical qubit may include communicatively coupling at least twoqubits as respective intermediate qubits communicatively coupled betweenthe first and the second outermost qubits; for at least one of the atleast one intermediate qubits of the logical qubit, communicativelycoupling an orthogonal control qubit to the respective intermediatequbit includes for each of the at least two intermediate qubits,communicatively coupling a respective orthogonal control qubit to therespective intermediate qubit; and programming at least some of theintermediate qubits to have respective values of the first programmableparameter higher than the first value. Communicatively coupling anorthogonal control qubit to the respective intermediate qubit mayinclude communicatively coupling the respective orthogonal control qubitdirectly to the respective intermediate qubit. Communicatively couplingan orthogonal control qubit to the respective intermediate qubit mayinclude communicatively coupling the respective orthogonal control qubitdirectly via a respective one of the couplers to the respectiveintermediate qubit. Communicatively coupling an orthogonal control qubitto the respective intermediate qubit may include communicativelycoupling the respective orthogonal control qubit which is smaller inarea than the respective intermediate qubit to the respectiveintermediate qubit. The first programmable parameter may be tunnelingamplitude, and programming the first programmable parameter of the firstand the second outermost qubits may include programming a respectivetunneling amplitude of the first and the second outermost qubits via theprogramming subsystem. The second programmable parameter may be apersistent current of the second qubit, and programming the tunnelingamplitude of the orthogonal control qubit may include programming arespective tunneling amplitude of the orthogonal control qubit via theprogramming subsystem without substantially affecting the persistentcurrent of the first and the second outermost qubits.

A quantum processor apparatus may be summarized as including a pluralityof qubits, each qubit having a respective first programmable parameterand a respective second programmable parameter that at least partiallydepends on the respective first programmable parameter, and a pluralityof coupling devices that each selectively provide communicative couplingbetween respective pairs of the qubits, wherein: at least three of thequbits are communicatively coupled to one another as a single logicalqubit, the single logical qubit formed by a first outermost qubit, asecond outermost qubit and at least one intermediary qubit, the at leastone intermediary qubit strongly communicatively coupled between thefirst and the second outermost qubits, the first outmost qubit being anoutermost qubit of the qubits of the logical qubit in a first directionalong a logical qubit path defined by the qubits of the logical qubitand the second outermost qubit being an outermost qubit in a seconddirection along the logical qubit path; for at least one of the at leastone intermediate qubits of the logical qubit, at least one of the qubitscommunicatively coupled as an orthogonal control qubit to the respectiveintermediate qubit such that the orthogonal control qubit is notcommunicatively coupled to any other qubit except via the respectiveintermediate qubit; the first and the second outermost qubits each havea respective first programmable parameters less than or equal to a firstvalue; and the orthogonal control qubit has a value of the firstprogrammable parameter higher than the first value. The single logicalqubit may include at least two qubits communicatively coupled betweenthe first and the second outermost qubits as respective intermediatequbits, and a respective orthogonal control qubit communicativelycoupling to each of the respective intermediate qubits. The singlelogical qubit may include at least two qubits communicatively coupledbetween the first and the second outermost qubits as respectiveintermediate qubits, and for each of the intermediate qubits, arespective orthogonal control qubit communicatively coupled to therespective intermediate qubit; and at least some of the intermediatequbits having respective values of the first programmable parameterhigher than the first value. The respective orthogonal control qubit maybe communicatively coupled directly to the respective intermediatequbit. The respective orthogonal control qubit may be directly via arespective one of the couplers to the respective intermediate qubit. Therespective orthogonal control qubit may be smaller in area than therespective intermediate qubit to the respective intermediate qubit. Thefirst programmable parameter may be tunneling amplitude, and arespective tunneling amplitude of the first and the second outermostqubits may be less than or equal to a first value. The secondprogrammable parameter may be a persistent current of the second qubit,and a respective tunneling amplitude of the orthogonal control qubit maynot substantially affect the persistent current of the first and thesecond outermost qubits.

The quantum processor apparatus may further include at least one firstprogramming subsystem communicatively coupleable to a compound Josephsonjunction of at least one of the qubits and operable to program atunneling amplitude of the at least one of the qubits; and at least onesecond programming subsystem communicatively coupleable to a qubit loopof at least one of the qubits and operable to program a persistentcurrent of the at least one of the qubits.

A method of controlling qubit parameters in a quantum processor, whereinthe quantum processor includes a plurality of qubits, each qubit havinga respective first programmable parameter and a respective secondprogrammable parameter that at least partially depends on the respectivefirst programmable parameter, and a plurality of coupling devices thateach selectively provide communicative coupling between respective pairsof the qubits may be summarized as including for at least a first qubit,communicatively coupling an orthogonal control qubit to the first qubitsuch that the orthogonal control qubit is not communicatively coupled toany other qubit except via the first qubit; for at least the firstqubit, communicatively coupling the first qubit to at least a secondqubit which is not the orthogonal control qubit; programming the firstqubits to have respective first programmable parameters less than orequal to a first value; and programming the orthogonal control qubit tohave a respective value of the first programmable parameter higher thanthe first value. Communicatively coupling an orthogonal control qubit tothe first qubit may include communicatively coupling the orthogonalcontrol qubit directly to the first qubit. Communicatively coupling anorthogonal control qubit to the first qubit may include communicativelycoupling the orthogonal control qubit directly via a respective one ofthe couplers to the first qubit. Communicatively coupling an orthogonalcontrol qubit to the first qubit may include communicatively couplingthe orthogonal control qubit which is smaller in area than the firstqubit to the first qubit. The first programmable parameter may betunneling amplitude, and programming the first programmable parameter ofthe first qubit may include programming a respective tunneling amplitudeof the first qubit via the programming subsystem. The secondprogrammable parameter may be a persistent current of the second qubit,and programming the tunneling amplitude of the orthogonal control qubitmay include programming a respective tunneling amplitude of theorthogonal control qubit via the programming subsystem withoutsubstantially affecting the persistent current of the first qubit.

A quantum processor apparatus may be summarized as including a pluralityof qubits, each qubit having a respective first programmable parameterand a respective second programmable parameter that at least partiallydepends on the respective first programmable parameter, and a pluralityof coupling devices that each selectively provide communicative couplingbetween respective pairs of the qubits, wherein: at least one of thequbits is communicatively coupled as an orthogonal control qubit to afirst qubit such that the orthogonal control qubit is notcommunicatively coupled to any other qubit except via the first qubit;the first qubit is communicatively coupled to at least a second qubitwhich is not the orthogonal control qubit; the first qubit has arespective first programmable parameter less than or equal to a firstvalue; and the orthogonal control qubit has a respective value of thefirst programmable parameter higher than the first value. The orthogonalcontrol qubit may be communicatively coupled directly to the firstqubit. The orthogonal control qubit may be communicatively coupleddirectly via a respective one of the couplers to the first qubit. Theorthogonal control qubit may be smaller in area than the first qubit tothe first qubit. The first programmable parameter may be tunnelingamplitude, and a respective tunneling amplitude of the first qubit maybe less than or equal to a first value. The second programmableparameter may be a persistent current of the second qubit, and arespective tunneling amplitude of the orthogonal control qubit may notsubstantially affect the persistent current of the first qubit.

The quantum processor apparatus may further include at least one firstprogramming subsystem communicatively coupleable to a compound Josephsonjunction of at least one of the qubits and operable to program atunneling amplitude of the at least one of the qubits; and at least onesecond programming subsystem communicatively coupleable to a qubit loopof at least one of the qubits and operable to program a persistentcurrent of the at least one of the qubits.

A method of controlling qubit parameters in a quantum processor, whereinthe quantum processor includes a plurality of qubits, each qubit havinga respective first programmable parameter and a respective secondprogrammable parameter that at least partially depends on the respectivefirst programmable parameter, and a plurality of coupling devices thateach provide communicative coupling between respective sets of at leasttwo qubits from the plurality of qubits may be summarized as includingcommunicatively coupling a first qubit from the plurality of qubits anda second qubit from the plurality of qubits via a first coupling devicefrom the plurality of coupling devices such that the first qubit, thesecond qubit, and the first coupling device collectively behave as afirst logical qubit having an effective first programmable parameterthat at least partially depends on the first programmable parameter ofthe first qubit and the first programmable parameter of the second qubitand an effective second programmable parameter that at least partiallydepends on the second programmable parameter of the first qubit and thesecond programmable parameter of the second qubit; and programming theeffective first programmable parameter of the first logical qubit via aprogramming subsystem, wherein programming the effective firstprogrammable parameter of the first logical qubit includes programmingthe first programmable parameter of the first qubit via the programmingsubsystem, wherein the first programmable parameter of the first qubitis independent of the second programmable parameter of the second qubitsuch that programming the first programmable parameter of the firstqubit does not substantially affect the second programmable parameter ofthe second qubit.

The method may further include communicatively coupling a third qubitfrom the plurality of qubits and either the first qubit from theplurality of qubits or the second qubit from the plurality of qubits viaa second coupling device from the plurality of coupling devices suchthat the first qubit, the second qubit, the third qubit, the firstcoupling device, and the second coupling device collectively behave asthe first logical qubit, wherein the effective first programmableparameter of the first logical qubit at least partially depends on thefirst programmable parameter of the third qubit and the effective secondprogrammable parameter of the first logical qubit at least partiallydepends on the second programmable parameter of the third qubit. Thefirst programmable parameter of the first qubit via the programmingsubsystem may include programming a tunneling amplitude of the firstqubit via the programming subsystem. The second programmable parameterof the second qubit a persistent current of the second qubit, andprogramming the tunneling amplitude of the first qubit via theprogramming subsystem may include programming the tunneling amplitude ofthe first qubit via the programming subsystem without substantiallyaffecting the persistent current of the second qubit. Programming theeffective first programmable parameter of the first logical qubit viathe programming subsystem may include programming an effective tunnelingamplitude of the first logical qubit via the programming subsystem. Theeffective first programmable parameter of the first logical qubit viathe programming subsystem may include programming the first programmableparameter of the second qubit via the programming subsystem, and thefirst programmable parameter of the second qubit may be independent ofthe second programmable parameter of the first qubit such thatprogramming the first programmable parameter of the second qubit via theprogramming subsystem does not substantially affect the secondprogrammable parameter of the first qubit. The first programmableparameter of the second qubit via the programming subsystem may includeprogramming a tunneling amplitude of the second qubit via theprogramming subsystem.

The method may further include programming the effective secondprogrammable parameter of the first logical qubit via the programmingsubsystem, wherein programming the effective second programmableparameter of the first logical qubit includes programming the secondprogrammable parameter of the first qubit via the programming subsystem,wherein the second programmable parameter of the first qubit isindependent of the first programmable parameter of the second qubit suchthat programming the second programmable parameter of the first qubitdoes not substantially affect the first programmable parameter of thesecond qubit.

The method may further include programming the effective secondprogrammable parameter of the first logical qubit via the programmingsubsystem, wherein programming the effective second programmableparameter of the first logical qubit includes programming the secondprogrammable parameter of the second qubit via the programmingsubsystem, and wherein programming the second programmable parameter ofthe second qubit does not substantially affect the first programmableparameter of the first qubit.

A quantum processor comprising a plurality of hybrid qubits may besummarized as including a respective first qubit comprising: a firstqubit loop formed by a first closed superconducting current path; and acompound Josephson junction that interrupts the first qubit loop; arespective second qubit comprising: a second qubit loop formed by asecond closed superconducting current path; a first Josephson junctionthat interrupts the second qubit loop; and a compound Josephson junctionthat interrupts the second qubit loop; a respective first programmingsubsystem communicatively coupleable to the compound Josephson junctionof the respective first qubit; a respective second programming subsystemcommunicatively coupleable to the first qubit loop of the respectivefirst qubit; and a respective third programming subsystemcommunicatively coupleable to the compound Josephson junction of therespective second qubit, wherein the second qubit loop of the respectivesecond qubit is galvanically coupled to the first qubit loop of therespective first qubit such that a portion of the second superconductingcurrent path includes a portion of the first superconducting currentpath and is shared between the first and second superconducting currentpaths and wherein the first Josephson junction that interrupts thesecond qubit loop interrupts the portion of the second superconductingcurrent path that is shared between the first and second superconductingcurrent paths.

Each respective second qubit may further include a second Josephsonjunction that interrupts the second qubit loop, and wherein the secondJosephson junction that interrupts the second qubit loop interrupts aportion of the second superconducting current path that is not sharedbetween the first and second superconducting current paths. Eachrespective first qubit may include a respective first programmableparameter that is controlled by the respective first programmingsubsystem communicatively coupleable to the compound Josephson junctionof the respective first qubit and a respective second programmableparameter that is controlled by the respective second programmingsubsystem communicatively coupleable to the first qubit loop of therespective first qubit, and wherein, for each respective first qubit,the respective second programmable parameter at least partially dependson the respective first programmable parameter. Each respective secondqubit may include a respective first programmable parameter that iscontrolled by the respective third programming subsystem communicativelycoupleable to the compound Josephson junction of the respective secondqubit, and wherein the respective second programmable parameter of eachrespective first qubit is independent of the respective firstprogrammable parameter of the respective second qubit to which therespective first qubit is galvanically coupled, such that the respectivefirst programmable parameter of each respective second qubit does notsubstantially affect the respective second programmable parameter of therespective first qubit to which the respective second qubit isgalvanically coupled. For each respective first qubit, the respectivefirst programmable parameter may be a respective tunneling amplitude ofthe respective first qubit and the respective second programmableparameter may be a respective persistent current in the first qubit loopof the respective first qubit, and, for each respective second qubit,the respective first programmable parameter may be a respectivetunneling amplitude of the respective second qubit.

The quantum processor wherein each hybrid qubit may further include arespective effective first programmable parameter that at leastpartially depends on the respective first programmable parameter of therespective first qubit and the respective first programmable parameterof the respective second qubit; and a respective effective secondprogrammable parameter that at least partially depends on the respectivesecond programmable parameter of the respective first qubit, such thateach hybrid qubit behaves as a respective logical qubit. For eachrespective hybrid qubit, the respective effective first programmableparameter may be an effective tunneling amplitude of the respectivehybrid qubit and the respective effective second programmable parametermay be an effective persistent current of the respective hybrid qubit.

The quantum may further include a plurality of coupling devices, whereineach respective coupling device is communicatively coupleable to arespective first qubit in a respective first hybrid qubit and arespective first qubit in a respective second hybrid qubit such thateach respective coupling device provides communicative coupling betweena respective pair of hybrid qubits. Each respective coupling device mayinclude a respective loop of superconducting material interrupted by atleast one respective Josephson junction, and each respective couplingdevice maybe communicatively coupleable to a respective first qubit in arespective first hybrid qubit via galvanic or inductive coupling and toa respective first qubit in a respective second hybrid qubit viagalvanic or inductive coupling. A first hybrid qubit and a second hybridqubit may be communicatively coupleable via a first coupling device tobehave as a first logical qubit including an effective firstprogrammable parameter that depends on the first programmable parameterof the first qubit in the first hybrid qubit, the first programmableparameter of the second qubit in the first hybrid qubit, the firstprogrammable parameter of the first qubit in the second hybrid qubit,and the first programmable parameter of the second qubit in the secondhybrid qubit; and an effective second programmable parameter thatdepends on the second programmable parameter of the first qubit in thefirst hybrid qubit and the second programmable parameter of the firstqubit in the second hybrid qubit, wherein the effective firstprogrammable parameter of the first logical qubit is independent of theeffective second programmable parameter of the first logical qubit suchthat the effective first programmable parameter of the first logicalqubit does not substantially affect the effective second programmableparameter of the first logical qubit.

A method of achieving orthogonal control of at least two effective qubitparameters in a quantum processor comprising a plurality of hybridqubits, wherein each hybrid qubit comprises a respective first qubithaving a respective first programmable parameter and a respective secondprogrammable parameter, and a respective second qubit having arespective first programmable parameter, the respective first qubit andthe respective second qubit of each respective hybrid qubit beinggalvanically coupled may be summarized as including programming aneffective first programmable parameter of a first hybrid qubit via aprogramming subsystem without substantially affecting an effectivesecond programmable parameter of the first hybrid qubit, wherein theeffective first programmable parameter of the first hybrid qubit dependson both the respective first programmable parameter of the respectivefirst qubit of the first hybrid qubit and the respective firstprogrammable parameter of the respective second qubit of the firsthybrid qubit and the effective second programmable parameter of thefirst hybrid qubit depends on the respective second programmableparameter of the respective first qubit of the first hybrid qubit, andwherein programming the effective first programmable parameter of thefirst hybrid qubit includes programming the respective firstprogrammable parameter of the respective second qubit of the firsthybrid qubit via the programming subsystem, wherein the respectivesecond programmable parameter of the respective first qubit of the firsthybrid qubit is independent of the respective first programmableparameter of the respective second qubit of the first hybrid qubit suchthat programming the respective first programmable parameter of therespective second qubit of the first hybrid qubit does not substantiallyaffect the respective second programmable parameter of the respectivefirst qubit of the first hybrid qubit. Programming the effective firstprogrammable parameter of the first hybrid qubit via the programmingsubsystem may include programming an effective tunneling amplitude ofthe first hybrid qubit, and programming the respective firstprogrammable parameter of the respective second qubit of the firsthybrid qubit via the programming subsystem may include programming atunneling amplitude of the respective second qubit via the programmingsubsystem. The respective second programmable parameter of therespective first qubit of the first hybrid qubit may be a persistentcurrent of the respective first qubit and wherein programming thetunneling amplitude of the respective second qubit may not substantiallyaffect the persistent current of the respective first qubit.

The method may further include communicatively coupling a second hybridqubit and the first hybrid qubit via a first coupling device such thatthe first hybrid qubit, the second hybrid qubit, and the first couplingdevice collectively behave as a single logical qubit, wherein the secondhybrid qubit includes: an effective first programmable parameter thatdepends on both the respective first programmable parameter of therespective first qubit of the second hybrid qubit and the respectivefirst programmable parameter of the respective second qubit of thesecond hybrid qubit; and an effective second programmable parameter thatdepends on the respective second programmable parameter of therespective first qubit of the second hybrid qubit, wherein the firstlogical qubit includes: an effective first programmable parameter thatdepends on both the effective first programmable parameter of the firsthybrid qubit and the effective first programmable parameter of thesecond hybrid qubit; and an effective second programmable parameter thatdepends on both the effective second programmable parameter of the firsthybrid qubit and the effective second programmable parameter of thesecond hybrid qubit.

The method may further include programming the effective firstprogrammable parameter of the first logical qubit via the programmingsubsystem, wherein programming the effective first programmableparameter of the first logical qubit includes programming at least oneof the effective first programmable parameter of the first hybrid qubitor the effective first programmable parameter of the second hybrid qubitvia the programming subsystem.

The method may further include programming the effective secondprogrammable parameter of the first logical qubit via the programmingsubsystem, wherein programming the effective second programmableparameter of the first logical qubit includes programming at least oneof the effective second programmable parameter of the first hybrid qubitor the effective second programmable parameter of the second hybridqubit via the programming subsystem.

A method of achieving orthogonal control of at least two qubitparameters in a quantum processor may be summarized as includingcommunicatively coupling a first qubit and a second qubit such that thefirst qubit and the second qubit together behave as a single logicalqubit, wherein the first qubit includes a first programmable parameterand a second programmable parameter, the second programmable parameterof the first qubit at least partially dependent on the firstprogrammable parameter of the first qubit, and wherein the second qubitincludes at least a first programmable parameter, the secondprogrammable parameter of the first qubit substantially independent ofthe first programmable parameter of the second qubit; and programming aneffective first programmable parameter of the logical qubit via aprogramming subsystem without substantially affecting an effectivesecond programmable parameter of the logical qubit, wherein theeffective first programmable parameter of the logical qubit at leastpartially depends on the first programmable parameter of the first qubitand the first programmable parameter of the second qubit and theeffective second programmable parameter of the logical qubit at leastpartially depends on the second programmable parameter of the firstqubit, and wherein programming the effective first programmableparameter of the logical qubit via the programming subsystem includesprogramming the first programmable parameter of the second qubit via theprogramming subsystem without substantially affecting the secondprogrammable parameter of the first qubit.

The method may further include programming the effective secondprogrammable parameter of the logical qubit via the programmingsubsystem, wherein programming the effective second programmableparameter of the logical qubit includes programming the secondprogrammable parameter of the first qubit via the programming subsystem.The first qubit may include a first qubit loop formed by a first closedsuperconducting current path and a first compound Josephson junctionthat interrupts the first qubit loop; the second qubit may include asecond qubit loop formed by a second closed superconducting current pathand a second compound Josephson junction that interrupts the secondqubit loop; and communicatively coupling the first qubit and the secondqubit such that the first qubit and the second qubit together behave asa single logical qubit may include communicatively coupling the firstqubit and the second qubit via a coupling device such that the firstqubit, the second qubit, and the coupling device collectively behave asa single logical qubit. Coupling the first qubit and the second qubitvia a coupling device such that the first qubit, the second qubit, andthe coupling device collectively behave as a single logical qubit mayinclude inductively coupling the first qubit and the coupling device andinductively coupling the second qubit and the coupling device. The firstqubit may include a first qubit loop formed by a first closedsuperconducting current path and a first compound Josephson junctionthat interrupts the first qubit loop; the second qubit may include asecond qubit loop formed by a second closed superconducting currentpath, a first Josephson junction that interrupts the second qubit loop,and a second compound Josephson junction that interrupts the secondqubit loop; and communicatively coupling the first qubit and the secondqubit such that the first qubit and the second qubit together behave asa single logical qubit may include galvanically coupling the first qubitloop of the first qubit and the second qubit loop of the second qubitsuch that a portion of the second superconducting current path includesa portion of the first superconducting current path and is sharedbetween the first and second superconducting current paths, and suchthat the first Josephson junction that interrupts that second qubit loopinterrupts the portion of the second superconducting current path thatis shared between the first and second superconducting current paths.The method wherein the second qubit may further include a secondJosephson junction that interrupts the second qubit loop; andcommunicatively coupling the first qubit and the second qubit such thatthe first qubit and the second qubit together behave as a single logicalqubit may include galvanically coupling the first qubit loop of thefirst qubit and the second qubit loop of the second qubit such that thesecond Josephson junction that interrupts the second qubit loopinterrupts a portion of the second superconducting current path that isnot shared between the first and second superconducting current paths.The effective first programmable parameter of the logical qubit via theprogramming subsystem may include programming an effective tunnelingamplitude of the logical qubit, and programming the first programmableparameter of the second qubit via the programming subsystem may includeprogramming a tunneling amplitude of the second qubit via theprogramming subsystem.

The second programmable parameter of the first qubit may be a persistentcurrent of the first qubit, and wherein programming the tunnelingamplitude of the second qubit via the programming subsystem may notsubstantially affect the persistent current of the first qubit.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

In the drawings, identical reference numbers identify similar elementsor acts. The sizes and relative positions of elements in the drawingsare not necessarily drawn to scale. For example, the shapes of variouselements and angles are not drawn to scale, and some of these elementsare arbitrarily enlarged and positioned to improve drawing legibility.Further, the particular shapes of the elements as drawn are not intendedto convey any information regarding the actual shape of the particularelements, and have been solely selected for ease of recognition in thedrawings.

FIG. 1 is a schematic diagram of an exemplary logical qubit from aportion of a superconducting quantum processor in accordance with thepresent systems and methods.

FIG. 2 is a flow-diagram of a method for controlling qubit parameters ina quantum processor that includes a plurality of qubits, in accordancewith the present systems and methods.

FIG. 3 is a schematic diagram of an exemplary hybrid qubit comprising afirst qubit and a second qubit galvanically coupled to the first qubitvia a Josephson junction, in accordance with the present systems andmethods.

FIG. 4 is a schematic diagram of a logical qubit comprising three hybridqubits and two tunable ZZ-couplers coupling information therebetween, inaccordance with the present systems and methods.

FIG. 5 is a flow-diagram of a method for achieving orthogonal control ofat least two non-orthogonal qubit parameters in a quantum processorcomprising a plurality of hybrid qubits, in accordance with the presentsystems and methods.

FIG. 6 is a flow-diagram of a general method for achieving orthogonalcontrol of at least two non-orthogonal qubit parameters in a quantumprocessor, in accordance with the present systems and methods.

FIG. 7 is a schematic diagram that illustrates an exemplary hybridcomputer including a digital processor and an analog processor inaccordance with the present systems and methods.

DETAILED DESCRIPTION

In the following description, certain specific details are set forth inorder to provide a thorough understanding of various disclosedembodiments. However, one skilled in the relevant art will recognizethat embodiments may be practiced without one or more of these specificdetails, or with other methods, components, materials, etc. In otherinstances, well-known structures associated with quantum processors,qubits, couplers, controller, readout devices and/or interfaces have notbeen shown or described in detail to avoid unnecessarily obscuringdescriptions of the embodiments.

Unless the context requires otherwise, throughout the specification andclaims which follow, the word “comprise” and variations thereof, suchas, “comprises” and “comprising” are to be construed in an open,inclusive sense, that is as “including, but not limited to.”

Reference throughout this specification to “one example”, “an example”,“one embodiment” or “an embodiment” means that a particular feature,structure or characteristic described in connection with the embodimentis included in at least one embodiment. Thus, the appearances of thephrases “in one example”, “in an example”, “in one embodiment” or “in anembodiment” in various places throughout this specification are notnecessarily all referring to the same embodiment. Furthermore, theparticular features, structures, or characteristics may be combined inany suitable manner in one or more embodiments.

As used in this specification and the appended claims, the singularforms “a,” “an,” and “the” include plural referents unless the contentclearly dictates otherwise. It should also be noted that the term “or”is generally employed in its sense including “and/or” unless the contentclearly dictates otherwise.

The headings and Abstract of the Disclosure provided herein are forconvenience only and do not interpret the scope or meaning of theembodiments.

Qubit chains may be used in quantum processors to embed problems intothe quantum hardware. Increasing the length of a qubit chain increasesthe effective connectivity of the qubit graph (at the cost of reducingthe number of effective qubits in the graph) which facilitates embeddingof problems into the quantum processor. It is typically difficult tobuild chains or sets longer (i.e., total number of qubits) than aboutfour qubits as the effective tunneling amplitude decreases exponentiallyas the size of the chain grows (see, for example, Equation 5). However,in accordance with the present systems and methods, the exponentialreduction of the effective tunneling amplitude as the number of qubitsin a chain grows can be avoided programmatically by applying specificconfigurations of individual qubit parameter signals. For example,according to Equation 5, if all qubits in a chain except for one haveΔ_(i)˜J_(i) and only one of the qubits has Δ_(i)=Δ, then the effectivetunneling amplitude Δ_(eff)˜Δ, which is no longer exponentiallydependent on the number of qubits in the chain.

Therefore, longer chains of qubits with a stable effective tunnelingamplitude can be achieved by using larger individual tunnelingamplitudes (Δ_(i)˜J_(i)) for the qubits that are inside the chain ofqubits (i.e., “inner qubits” that are not actively coupled to any qubitsoutside of the chain) and lower individual tunneling amplitudes(Δ_(i)=Δ) for the qubits that are coupled to qubits that are outside ofthe chain (e.g., qubits that are at the ends of the chain, and/or anyqubit(s) in the middle of the chain that are actively coupled to a qubitor qubits that are not part of the chain). This way the effectivetunneling amplitude of all logical qubits, including those representedby chains of qubits, will be stabilized, leading to better performance.

Adjusting the individual tunneling amplitude of a qubit may change thepersistent current of the qubit which may then change the programmableparameters (such as h and J) of the qubit. This unintentional change ofthe programmable parameters of a superconducting qubit arises becausethe persistent current and the tunneling amplitude of a superconductingqubit are non-orthogonal parameters and results in the quantum processorsolving erroneous problems. Of the various embodiments described hereinprovide systems and methods for achieving orthogonal control ofnon-orthogonal qubit parameters by, for example, introducing a secondqubit communicatively coupled to a first qubit so that the pair ofcommunicatively coupled qubits may behave as a single logical qubit. Ifeach of the qubits in the logical qubit has a tunneling amplitude Δ_(i)and the coupling between the pair of qubits is J, the effectivetunneling amplitude of the logical qubit in the perturbative regime ofΔ<<J is:

$\begin{matrix}{\Delta_{eff}\text{∼}\frac{\Delta_{1}\Delta_{2}}{J}} & (3)\end{matrix}$Therefore, by adjusting the tunneling amplitude of one qubit, theeffective tunneling amplitude of the logical qubit can be adjusted. Forexample, tuning the tunneling amplitude of the second qubit will adjustthe effective tunneling amplitude of the logical qubit without affectingthe persistent current of the first qubit. Orthogonal control ofnon-orthogonal qubit parameters can therefore be achieved bycommunicatively coupling a second qubit to a first qubit to form asingle logical qubit, where a first effective parameter of the logicalqubit is adjusted by adjusting a first parameter of the first qubit anda first parameter of the second qubit and a second effective parameterof the logical qubit is adjusted by adjusting a second parameter of thefirst qubit, and where the first parameter of the first qubit and thesecond parameter of the second qubit do not influence one another.Longer chains of qubits can therefore be achieved by forming chains ofsuch logical qubit pairs.

Throughout this specification and the appended claims, the term “logicalqubit” is used to describe a collection/chain of communicatively coupledqubits that act as a single qubit. In other words, a chain ofcommunicatively coupled qubits that may collectively represent a singlevariable of a problem may be referred to as a logical qubit. Therefore,a logical qubit may comprise more than one qubit. However, a chain ofcommunicatively coupled qubits may not always be a logical qubit as theindividual qubits in the chain of qubits may represent differentvariables of a problem. When a chain of qubits are programmed torepresent a single variable such that the chain of qubits collectivelyact as a single qubit, that chain of qubits may then be called a logicalqubit. According to the present systems and methods, a logical qubit mayat least be formed by communicatively coupling a first qubit to a secondqubit such that the first qubit and the second qubit collectively behaveas one qubit.

The various embodiments described herein provide systems and methods forachieving orthogonal control of non-orthogonal qubit parameters andthereby increase the number of qubits that can be communicativelycoupled to behave as a single logical qubit. As an illustrative example,a superconducting quantum processor designed to perform adiabaticquantum computation and/or quantum annealing is used in the descriptionthat follows. However, a person of skill in the art will appreciate thatthe present systems and methods may be applied to any form of quantumprocessor hardware implementing any form of quantum algorithm(s) (e.g.,adiabatic quantum computation, quantum annealing, gate/circuit-basedquantum computing, etc.).

An evolution Hamiltonian is proportional to the sum of a first termproportional to the problem Hamiltonian and a second term proportionalto the disordering Hamiltonian. As previously discussed, a typicalevolution may be represented by Equation 7:H _(E) ∝A(t)H _(D) +B(t)H _(P)  (7)where H_(P) is the problem Hamiltonian, disordering Hamiltonian isH_(D), H_(E) is the evolution or instantaneous Hamiltonian, and A(t) andB(t) are examples of an evolution coefficient which controls the rate ofevolution. In general, evolution coefficients vary from 0 to 1. In someembodiments, a time varying envelope function is placed on the problemHamiltonian. A common disordering Hamiltonian is shown in Equation 8:

$\begin{matrix}{H_{D} \propto {{- \frac{1}{2}}{\sum\limits_{i = 1}^{N}{\Delta_{i}\sigma_{i}^{x}}}}} & (8)\end{matrix}$where N represents the number of qubits, σ_(i) ^(x) is the Paulix-matrix for the i^(th) qubit and Δ_(i) is the single qubit tunnelsplitting induced in the i^(th) qubit. Here, the σ_(i) ^(x) terms areexamples of “off-diagonal” terms. A common problem Hamiltonian includesfirst component proportional to diagonal single qubit terms and a secondcomponent proportional to diagonal multi-qubit terms. The problemHamiltonian, for example, may be of the form:

$\begin{matrix}{H_{P} \propto {- {\frac{ɛ}{2}\lbrack {{\sum\limits_{i = 1}^{N}{h_{i}\sigma_{i}^{z}}} + {\sum\limits_{j > i}^{N}{J_{ij}\sigma_{i}^{z}\sigma_{j}^{z}}}} \rbrack}}} & (9)\end{matrix}$where N represents the number of qubits, σ_(i) ^(z) is the Pauliz-matrix for the i^(th) qubit, h_(i) and J_(i,j), are dimensionlesslocal fields for the qubits, and couplings between qubits, and ε is somecharacteristic energy scale for H_(P). Here, the σ_(i) ^(z) and σ_(i)^(z)σ_(j) ^(z) terms are examples of “diagonal” terms. The former is asingle qubit term and the latter a two qubit term. Throughout thisspecification, the terms “problem Hamiltonian” and “final Hamiltonian”are used interchangeably. Hamiltonians such as H_(D) and H_(P) inEquations 8 and 9, respectively, may be physically realized in a varietyof different ways. A particular example is realized by an implementationof superconducting qubits.

FIG. 1 shows an exemplary logical qubit 100 from a portion of asuperconducting quantum processor in accordance with the present systemsand methods. Logical qubit 100 comprises three superconducting fluxqubits 101, 102, 103 and two tunable ZZ-couplers 111, 112 couplinginformation therebetween. While logical qubit 100 shown in FIG. 1includes three qubits 101, 102, 103 and two couplers 111, 112 those ofskill in the art will appreciate that logical qubit 100 may include anynumber of qubits, and any number of coupling devices couplinginformation therebetween (for example, 2 qubits and 1 coupling device, 5qubits and 4 coupling devices, etc.).

Each qubit 101, 102, 103 of logical qubit 100 has a respective firstprogrammable parameter and a respective second programmable parameter.The respective first programmable parameter of each qubit 101, 102, 103may for example be a tunneling amplitude of each qubit 101, 102, 103 andthe respective second programmable parameter of each qubit 101, 102, 103may for example be a persistent current of each qubit 101, 102, 103.However, a person of skill in the art will appreciate that, inalternative embodiments, the first and second programmable parameters ofa qubit may be any other programmable parameters of that qubit. Logicalqubit 100 has an effective first programmable parameter and an effectivesecond programmable parameter. The effective first programmableparameter of logical qubit 100 may depend on the respective firstprogrammable parameters of qubits 101, 102 and 103. The effective secondprogrammable parameter of logical qubit 100 may depend on the respectivesecond programmable parameters of qubits 101, 102 and 103. The effectivefirst programmable parameter of logical qubit 100 may, for example, bean effective tunneling amplitude of logical qubit 100 that is dependenton the respective tunneling amplitudes of qubits 101, 102, and 103,whereas the effective second programmable parameter of logical qubit 100may, for example, be an effective persistent current of logical qubit100 that is dependent on the respective persistent currents of qubits101, 102, and 103.

However, a person of skill in the art will appreciate that inalternative embodiments the effective first and second programmableparameters of a logical qubit may be any other effective programmableparameters of the logical qubit which depends on the respectiveprogrammable parameters of the individual qubits that make up thelogical qubit.

In order to adjust/maintain the effective tunneling amplitude of logicalqubit 100, the respective tunneling amplitudes of qubits 101,102 and 103may be adjusted. The respective tunneling amplitudes of qubits 101, 102and 103 may be adjusted by programming the barrier height of each qubit101, 102 and 103 via respective programming subsystems 121, 123 and 125.The respective persistent currents of qubits 101, 102 and 103 may beadjusted by a respective magnetic flux coupled into the body of eachrespective qubit 101, 102 and 103 via a respective programming subsystem122, 124 and 126. Programming subsystems 121-126 that are used toconfigure and control the programmable parameters of qubits 101, 102 and103 may be realized by respective inductive coupling structures, asillustrated, connected to a programming system (not shown). In theoperation of logical qubit 100, programming subsystems 121, 123 and 125may each be used to couple a flux signal ϕ_(CJJ) into a respectivecompound Josephson junction 131, 132, 133 of qubits 101, 102 and 103,thereby realizing the Δ_(i) terms (i.e., tunneling amplitude) in thesystem Hamiltonian. This coupling provides the σ^(x) terms of Equation8. Similarly, programming subsystems 122, 124 and 126 may each be usedto couple a flux signal ϕ_(X) into a respective qubit loop of qubits101, 102 and 103, thereby realizing the h_(i) terms in the systemHamiltonian. This coupling provides the σ^(z) terms of Equation 9.

Programming subsystem 141 may be used to control the coupling betweenqubits 101 and 102 realized by coupling device 111 and programmingsubsystem 142 may be used to control the coupling between qubits 102 and103 realized by coupling device 112.

The effective tunneling amplitude of logical qubit 100 may also beadjusted by adjusting the inductance L applied to at least one of qubits101, 102, 103 via for example, an inductance-tuner (referred tohereinafter as an “L-tuner”). In other words, by adjusting the L-tunersettings of at least one of qubits 101, 102, 103 to achieve anessentially similar effect as coupling a flux signal ϕ_(CJJ) into arespective compound Josephson junction 131, 132, 133 of qubits 101, 102and 103 as described above, the effective tunneling amplitude of logicalqubit 100 may be adjusted. FIG. 1 shows an L-tuner compound Josephsonjunction structure 181 connected in series with qubit 101 to enabletuning of the qubit inductance. The Josephson inductance of L-tunercompound Josephson junction structure 181 of qubit 101 may be tunedusing programming subsystem 191. Only L-tuner compound Josephsonjunction structure 181 and its corresponding programming subsystem 191is shown in FIG. 1 to reduce clutter. L-tuners are described in detailin, for example, US Patent Publication 2011-0057169.

As previously described, a plurality of qubits may be communicativelycoupled via a plurality of coupling devices (e.g., pair-wise coupled toform a chain or sequence, series or linear set of qubit-to-qubitcommunicatively coupled qubits which define a communicative path) inorder to form a logical qubit comprising a desired number of qubits andcoupling devices. The longer the logical qubit (i.e., the greater thenumber of qubits in a logical qubit), the greater the number of otherqubits communicatively coupleable with the logical qubit. In otherwords, increasing the number of qubits in a logical qubit increases theeffective connectivity of the logical qubit. However, in practice, it isdifficult to form logical qubits (or, in other words, chains of qubitswhere the qubits in a chain of qubits collectively represent a singlevariable) comprising more than four qubits. The exponential dependencybetween the effective tunneling amplitude of a logical qubit and thenumber of qubits in the logical qubit as given in Equation 5 lowers theeffective tunneling amplitude of the logical qubit to a point at whichthe qubits in the logical qubit may transition from the quantum regimeinto the classical regime and behave as classical bits. In accordancewith the present systems and methods, the decreasing effective tunnelingamplitude of a logical qubit due to increasing the number of qubits inthe logical qubit, for ferromagnetically coupled qubits, may becircumvented by programming a larger tunneling amplitude into theindividual qubits that are inside the logical qubit (i.e., “innerqubits”) than the tunneling amplitude of the individual qubits that areat the ends of the logical qubit. In other words, by applying a largertunneling amplitude into the individual qubits comprised in the logicalqubit that are inside the logical qubit (for example, qubit 102) thanthe tunneling amplitude of the outermost qubits of the logical qubit(for example, qubits 101 and 103), the otherwise decreasing effectivetunneling amplitude of the logical qubit due to addition of qubits tothe logical qubit may be avoided.

For example, in logical qubit 100, one may tune the individual tunnelingamplitudes of qubits that have an h approximately equal to zero and thatare not coupled to qubits that are outside the chain of qubits (i.e.,that are not coupled to qubits that do not belong to logical qubit 100)unless otherwise a careful calibration is done. Tuning the tunnelingamplitude of qubits that have a non-zero h value may alter thepersistent current of the logical qubit, and tuning the tunnelingamplitude of qubits that are actively coupled to at least one otherqubit outside of the chain may alter the persistent current of the otherqubits that are coupled to that qubit. Typically, adjusting thetunneling amplitude of a qubit changes the persistent current of thequbit which then changes the h and J of that qubit. However, if the h ofan individual qubit in a logical qubit is approximately zero and theinternal J of that qubit is large (i.e., strong coupling between thequbit and other qubits of the same logical qubit coupled to that qubit),changes in persistent current may only slightly affect the h and J ofthat qubit which gives the freedom to adjust the tunneling amplitude ofthat qubit. The inner qubits of a chain (for example, qubit 102 inFIG. 1) may be deliberately programmed to have approximately zero h. Thetunneling amplitude of such inner qubits may be adjusted to have atunneling amplitude that is higher than the tunneling amplitude of theother qubits in the chain, such that the effective tunneling amplitudeof the logical qubit may be, for example, substantially matched to theindividual tunneling amplitudes of qubits that are not part of thelogical qubit despite the fact that the logical qubit comprises multiplequbits. In other words, the exponential decrease in the effectivetunneling amplitude of a logical qubit (as per Equation 5) may beovercome by programming higher individual tunneling amplitudes into theinner qubits that make up the logical qubit. As a result, the logicalqubit remains in the quantum regime during the performance of quantumcomputations. In other words, by adjusting the tunneling amplitude ofsome selected qubits in a logical qubit, a uniform effective tunnelingamplitude of the logical qubit may be achieved.

FIG. 2 shows a method 200 for controlling qubit parameters in a quantumprocessor that includes a plurality of qubits, in accordance with thepresent systems and methods. Each qubit in the plurality of qubitscomprises a respective tunneling amplitude and a respective persistentcurrent. The quantum processor also includes a plurality of couplingdevices used to communicatively couple pairs of qubits together. Method200 includes two acts 201 a and 202 and an optional act 201 b, thoughthose of skill in the art will appreciate that in alternativeembodiments certain acts may be omitted and/or additional acts may beadded. Those of skill in the art will appreciate that the illustratedorder of the acts is shown for exemplary purposes only and may change inalternative embodiments.

At 201 a, a first qubit and a second qubit are communicatively coupledtogether via a first coupling device so that the first qubit, the secondqubit and the first coupling device collectively behave as a firstlogical qubit having an effective first programmable parameter and aneffective second programmable parameter. As previously described, thefirst and second effective programmable parameters of the first logicalqubit may be an effective tunneling amplitude and an effectivepersistent current of the logical qubit, respectively. The first qubitand the second qubit are communicatively coupled together via a firstcoupling device as illustrated in FIG. 1. For example, qubit 101 and 102of FIG. 1 are communicatively coupled together via coupling device 111as described in act 201 a. Communicatively coupling the first and thesecond qubit may include ferromagnetically, anti-ferromagneticallyand/or transversely coupling the first and the second qubit.

At 202, the effective first programmable parameter of the first logicalqubit of step 201 a is programmed via a programming subsystem. Eachqubit (for example, the first qubit and the second qubit) may comprise arespective first programmable parameter and a respective secondprogrammable parameter. The effective first programmable parameter ofthe logical qubit may be programmed by programming the firstprogrammable parameter of the first qubit, the first programmableparameter of the second qubit, or the respective first programmableparameters of both the first and second qubits via the programmingsubsystem (for example, programming subsystem 121 of FIG. 1). Theeffective first programmable parameter of the logical qubit may be aneffective tunneling amplitude of the logical qubit, the firstprogrammable parameter of the first qubit may be a tunneling amplitudeof the first qubit, and the first programmable parameter of the secondqubit may be a tunneling amplitude of the second qubit. The effectivesecond programmable parameter of the logical qubit may be an effectivepersistent current of the logical qubit, the second programmableparameter of the first qubit may be a persistent current of the firstqubit, and the second programmable parameter of the second qubit may bea persistent current of the second qubit.

At 201 b, a third qubit is communicatively coupled to the first qubit orthe second qubit of act 201 a via a second coupling device so that thefirst qubit, the second qubit, the third qubit, the first couplingdevice and the second coupling device may collectively behave as thefirst logical qubit of step 201 a. For example, FIG. 1 shows qubit 103communicatively coupled to qubit 102 via coupling device 112 such thatqubits 101, 102, 103 and coupling devices 111, 112 may collectivelybehave as logical qubit 100. Similar to act 202 and FIG. 1, a pluralityof qubits may be communicatively coupled via a plurality of couplingdevices in order to form a logical qubit comprising a desired number ofqubits and coupling devices. Therefore, act 201 b is an optional actthat may be carried out to form a logical qubit.

In order to maintain the effective tunneling amplitude of the logicalqubit that may otherwise decrease due to the addition of qubits to formthe logical qubit, the tunneling amplitudes of at least some of theindividual qubits in the logical qubit may be adjusted. In other words,the tunneling amplitudes of at least some of the individual qubits inthe logical qubit may be adjusted such that the effective tunnelingamplitude of the logical qubit may be substantially similar to theeffective tunneling amplitude of the logical qubit before the additionof additional qubits to form the logical qubit. Therefore, a targeteffective tunneling amplitude may be chosen to which the effectivetunneling amplitude of the logical qubit may be synchronized prior toadjusting the tunneling amplitudes of the individual qubits in thelogical qubit. As described in FIG. 1 above, tunneling amplitudes of“inner qubits” that are inside the chain of qubits (i.e., not at theends of the chain, sequence, series or linear set of qubits, e.g., qubit102 of logical qubit 100) and that have approximately zero h may beadjusted to modify the effective tunneling amplitude of the logicalqubit. For example, increasing the tunneling amplitude of an inner qubitwith an approximately zero h may compensate the decrease in theeffective tunneling amplitude of the logical qubit that results fromincluding that inner qubit in the chain, thereby maintaining theeffective tunneling amplitude of the logical qubit in the quantumregime. Changing the tunneling amplitude of a qubit with anapproximately zero h may not significantly affect the persistent currentof that qubit, and therefore may not significantly affect the h and Jparameters of that qubit. For this reason, it may be advantageous toadjust the tunneling amplitudes of qubits that are not actively coupledto qubits outside of the chain and that have an approximately zero h.

The tunneling amplitude of an inner qubit with a non-zero h may beadjusted with the addition of a second qubit strongly coupled to theinner qubit such that the change of tunneling amplitude of the secondqubit may not affect the persistent current of the inner qubit andtherefore may not affect the h and J values of the inner qubit. Thesecond qubit may, for example, be only actively or operablycommunicatively coupleable directly (i.e., with no intervening qubits,whether via a coupler or not) to the inner qubit, and not directlycoupled to any other qubit (i.e., the second qubit may have an“effective connectivity” of one). In this configuration, the combinationof the inner qubit and the second qubit may be referred to as a single“hybrid” qubit. This hybrid qubit is not necessarily a charge-phasequbit where the Josephson and charging energies are comparable.

A hybrid qubit may also be a logical qubit. A hybrid qubit may comprisea first qubit and a second qubit communicatively coupled to the firstqubit, the second qubit may be directly (i.e., with no interveningqubits, whether via a coupler or not) coupled to the first qubit only,and the second qubit may be made smaller than the first qubit. The mainrole of the second qubit of a hybrid qubit may be to adjust an effectiveprogrammable parameter of the hybrid qubit without affecting anothereffective programmable parameter of the hybrid qubit (i.e., achievingorthogonal control of non-orthogonal qubit parameters) hence denominatedherein and in the claims as an adjustment or an orthogonal controlqubit. The second qubit (i.e., adjustment or orthogonal control qubit)of a hybrid qubit may be galvanically coupled to the first qubit or itmay be inductively coupled.

A chain of qubits comprising a first qubit communicatively coupled to asecond qubit such that the chain of qubits may collectively behave as alogical qubit may not necessarily be a hybrid qubit. As used herein andin the claims, the term chain of qubits refer to sequences, series orlinear sets of pair-wised communicatively coupled qubits, which termsare used interchangeably herein. The qubits in the chain define or forma communicative path, from one outermost qubit to another outermostqubit, passing through one or more intermediary qubits and couplers. Oneof the outermost qubits is disposed in a first direction along thecommunicative path from the intermediary qubit(s), while the other oneof the outermost qubits is disposed in a second direction along thecommunicative path from the intermediary qubit(s). The directions arewith respect to a topology or geodesic defined by the communicativepath, which may or may not be a Cartesian coordinate system. As usedherein and in the claims the term directly coupled when used withrespect to communicative coupling between two or more qubits, means apair-wise communicative coupling between qubits, with no interveningqubits, whether those qubits are communicative coupled via one or morecouplers or not.

A notable difference between such a chain of qubits comprising a firstqubit and a second qubit communicatively coupled together and a hybridqubit comprising a first qubit and an adjustment or orthogonal controlqubit communicatively coupled to the first qubit is that each of thefirst qubit and the second qubit in a chain of qubits may also becommunicatively coupled to at least another qubit for example, toincrease the length of the chain of qubits. Whereas in a hybrid qubit,the first qubit may be communicatively coupled to the second qubit andto at least one other qubit, while the second or adjustment ororthogonal control qubit of the hybrid qubit may only be communicativelydirectly (i.e., with no intervening qubits, whether via a coupler ornot) coupled to the first qubit of the hybrid qubit and communicativelydirectly coupled to no other qubits. That is, the adjustment ororthogonal control qubit is not communicatively coupled to any otherqubits except possibly through the first qubit, thus having an“effective connectivity” of 1. In this respect, it is noted thatconnectivity has been used to refer to the maximum number of connectionspossible, assuming each coupler is active. “Effective connectivity” isused to refer to the fact that in use, the adjustment or orthogonalcontrol qubit is not communicatively coupled between other qubits, butrather communicatively directly coupled (i.e., with no interveningqubits, whether via a coupler or not) to a single qubit, for instancegalvanically or via a coupler, and other communicatively coupling beingvia the single qubit.

Therefore, unlike a chain, sequence, series or linear set of qubitscomprising at least a first qubit and a second qubit communicativelycoupled together, any of which may also be coupled to at least one otherqubit, a hybrid qubit comprises a first qubit and a dedicated secondqubit (i.e., the adjustment or orthogonal control qubit) communicativelycoupled to the first qubit. As such, the adjustment or orthogonalcontrol qubit of a hybrid qubit may act as a supporting member to thefirst qubit of the hybrid qubit such that an effective programmableparameter of the hybrid qubit may be adjusted by adjusting thecorresponding programmable parameter of the adjustment or orthogonalcontrol qubit. The first qubit of a hybrid qubit may be communicativelycoupled to the first qubit of another hybrid qubit such that the twohybrid qubits may act as a single logical qubit. Therefore, throughoutthis specification and the appended claims, a hybrid qubit comprising afirst qubit and a second qubit (i.e., adjustment or orthogonal controlqubit) communicatively coupled to the first qubit as well as a pluralityof hybrid qubits where the first qubit of each hybrid qubit may becommunicatively coupled the first qubit of another hybrid qubit therebyforming a chain of communicatively coupled hybrid qubits programmed tobehave as a single qubit may also be a logical qubit. In other words, achain of qubits acting as a single qubit, a hybrid qubit as well as aplurality of communicatively coupled hybrid qubits acting as a singlequbit may be called a logical qubit as in all three scenarios, a set ofqubits are used to represent a single variable and therefore the set ofqubits essentially behave as one qubit.

FIG. 3 shows an exemplary hybrid qubit 300 comprising first qubit 301and second or adjustment or orthogonal control qubit 351 galvanicallycoupled to first qubit 301 via Josephson junction 341, in accordancewith the present systems and methods. First qubit 301 maycommunicatively couple to other qubits in a quantum processor comprisinga plurality of qubits (e.g., a plurality of hybrid qubits) while secondor adjustment or orthogonal control qubit 351 may only couple to firstqubit 301.

First qubit 301 of hybrid qubit 300 may have an associated tunnelingamplitude and a persistent current. First qubit 301 comprises a loop ofsuperconducting material interrupted by compound Josephson junction 331.Second or adjustment or orthogonal control qubit 351 may also have anassociated tunneling amplitude and a persistent current. Second oradjustment or orthogonal control qubit 351 comprises a loop ofsuperconducting material interrupted by compound Josephson junction 361and at least one Josephson junction (for example, Josephson junctions341,342, 343). At least one Josephson junction 341 interrupts both theloop of superconducting material of first qubit 301 and the loop ofsuperconducting material of second or adjustment or orthogonal controlqubit 351. In other words, first qubit 301 and second or adjustment ororthogonal control qubit 351 are galvanically coupled together and atleast one Josephson junction 341 is shared by both first qubit 301 andsecond or adjustment or orthogonal control qubit 351. The tunnelingamplitude of first qubit 301 may be adjusted by a flux signal ϕ_(CJJ1)coupled into compound Josephson junction 331 via programming subsystem321. Similarly, the tunneling amplitude of second or adjustment ororthogonal control qubit 351 may be adjusted by a flux signal ϕ_(CJJ2)coupled into compound Josephson junction 361 via programming subsystem323. The persistent current of first qubit 301 may be adjusted by a fluxsignal ϕ_(X) coupled into the body of first qubit 301 via programmingsubsystem 322. Each of programming subsystems 321-323 may be realized bya respective inductive coupling structure, as illustrated, controlled bya programming system (not shown). Such a programming system may beseparate from the quantum processor (not shown), or it may be includedlocally (i.e., on-chip with quantum the processor), for example, asdescribed in U.S. Pat. Nos. 7,876,248 and 8,035,540. The tunnelingamplitude of first qubit 301 and the tunneling amplitude of second oradjustment or orthogonal control qubit 351 together define an effectivetunneling amplitude of hybrid qubit 300. Although hybrid qubit 300comprises first qubit 301 galvanically coupled to second or adjustmentor orthogonal control qubit 351, in alternative embodiments, first qubit301 may be communicatively coupled to second or adjustment or orthogonalcontrol qubit 351 either via a coupling device such that first qubit301, second or adjustment or orthogonal control qubit 351, and thecoupling device collectively behave as hybrid qubit 300, or without acoupling device and via direct inductive coupling that stronglymagnetically couples first qubit 301 and second or adjustment ororthogonal control qubit 351 together. However, an advantage ofgalvanically coupling second or adjustment or orthogonal control qubit351 to first qubit 301 as shown in FIG. 3 is a strong communicativecoupling established between first qubit 301 and second or adjustment ororthogonal control qubit 351 and reduced noise susceptibility. Althoughsecond or adjustment or orthogonal control qubit 351 comprises compoundJosephson junction 361 that may provide a tunable tunneling amplitude,in alternative embodiments, compound Josephson junction 361 may bereplaced with a single Josephson junction in parallel connection with atunable capacitor. However, adding a capacitor to replace compoundJosephson junction 361 may add unwanted noise to hybrid qubit 300 andtherefore may require additional structures to shield and/or reducenoise generated from the tunable capacitor. Josephson junctions ofsecond or adjustment or orthogonal control qubit 351 such as Josephsonjunctions 342, 343 may provide the necessary inductance to stronglycouple second or adjustment or orthogonal control qubit 351 to firstqubit 301. Without Josephson junctions 342, 343, the structure of secondor adjustment or orthogonal control qubit 351 may need to be larger (forexample, by increasing the qubit loop length of second or adjustment ororthogonal control qubit 351) in order to achieve the necessaryinductance. Therefore, forming Josephson junctions 342, 343 in second oradjustment or orthogonal control qubit 351 reduces the size (e.g., area,perimeter) of second or adjustment or orthogonal control qubit 351.

As previously described, the tunneling amplitude of a qubit may decreasewhen the qubit is communicatively coupled to another qubit or to a chainof communicatively coupled qubits in order to form a logical qubit. Thedecreasing tunneling amplitude may bring the qubit or logical qubit outof the quantum regime and into the classical regime, which disruptsnormal operation of the quantum processor. Adjusting the tunnelingamplitude of a qubit may affect the persistent current of that qubitwhich thereby changes qubit parameters such as the h and J terms of thatqubit. Such changes made to the qubit parameters (for example, h and J)may be undesirable as the resulting problem embedded into the qubits ofthe quantum processor may not end up being the problem solved by thequantum processor since the parameters have changed or may be solvedincorrectly. Therefore, the tunneling amplitude of a qubit (in, forexample, a chain of qubits) needs to be adjusted/increased withoutaffecting its persistent current.

Adjusting the tunneling amplitude of second or adjustment or orthogonalcontrol qubit 351 of hybrid qubit 300 such that the tunneling amplitudeof second or adjustment or orthogonal control qubit 351 is very largecompared to the tunneling amplitude of first qubit 301 of hybrid qubit300 ensures that the effective tunneling amplitude of hybrid qubit 300is dominated by the tunneling amplitude of second or adjustment ororthogonal control qubit 351. Therefore, by only adjusting the tunnelingamplitude of second or adjustment or orthogonal control qubit 351, theeffective tunneling amplitude of hybrid qubit 300 may be adjusted ormaintained.

The effective persistent current of hybrid qubit 300 may, at least inpart depend on the persistent current of first qubit 301 withoutrestricting the persistent current of second or adjustment or orthogonalcontrol qubit 351. In the example of FIG. 3, the effective persistentcurrent of hybrid qubit 300 is given by the persistent current of firstqubit 301. The effective persistent current of hybrid qubit 300 is notsubstantially affected by the adjustment of the effective tunnelingamplitude of hybrid qubit 300 via an adjustment to the tunnelingamplitude of second or adjustment or orthogonal control qubit 351. Thus,the combination of first qubit 301 and second or adjustment ororthogonal control qubit 351 illustrated in FIG. 3 provides a hybridqubit 300 having orthogonal control of two non-orthogonal effectiveprogrammable parameters: effective persistent current and effectivetunneling amplitude. Furthermore, since second or adjustment ororthogonal control qubit 351 does not need to couple to anything otherthan first qubit 301, second or adjustment or orthogonal control qubit351 does not need a large inductance and hence can be made physicallysmaller in size (e.g., area, perimeter) than first qubit 301. Multiplesecond qubits 351 may not take up a large portion of the chip area in aquantum processor comprising a plurality of similar hybrid qubits 300.

A logical qubit may be formed by communicatively coupling together atleast two qubits as illustrated in FIG. 1. Similarly, in accordance withthe present systems and methods, a logical qubit may be formed bycommunicatively coupling together at least two hybrid qubits (i.e.,coupling a first hybrid qubit 300 to another hybrid qubit). This mayallow for forming logical qubits with an increased number ofcommunicatively coupled qubits (i.e., a longer chain of qubits) witheach hybrid qubit comprising a tunable effective tunneling amplitude.

As described in FIG. 3, a hybrid qubit may comprise a first qubit and asecond or adjustment or orthogonal control qubit galvanically coupled tothe first qubit. The first qubit may comprise a loop of superconductingmaterial interrupted by at least one Josephson junction. The second oradjustment or orthogonal control qubit may also comprise a loop ofsuperconducting material interrupted by at least one Josephson junction.The second or adjustment or orthogonal control qubit loop may be smallerin size than the first qubit loop and hence have a very small inductancecompared to the first qubit loop. The second or adjustment or orthogonalcontrol qubit may be galvanically coupled to the first qubit via a largecommon Josephson junction with a single programming subsystem used toprogram a programmable parameter of the second qubit such as tunnelingamplitude. Due to reduced size and therefore inductance, the second oradjustment or orthogonal control qubit may not produce a large magneticflux and it may not couple to flux noise significantly and therefore, itadvantageously may not reduce the decoherence time of the first qubit.Furthermore, the second or adjustment or orthogonal control qubit maynot affect the capacitance of the first qubit. Having a second oradjustment or orthogonal control qubit galvanically coupled to the firstqubit to form a hybrid qubit allows for achieving orthogonal control ofotherwise non-orthogonal qubit parameters. For example, in order toadjust the effective tunneling amplitude of a hybrid qubit, only thetunneling amplitude of the second or adjustment or orthogonal controlqubit may be adjusted. The tunneling amplitude of the second oradjustment or orthogonal control qubit may be very large so that itdominates the tunneling amplitude of the first qubit. The persistentcurrent of the first qubit may not be substantially affected by thetunneling amplitude of the second or adjustment or orthogonal controlqubit. Therefore, the second or adjustment or orthogonal control qubitof a hybrid qubit may act as a supporting member of the first qubit. Ahybrid qubit may be a part of a larger system of hybrid qubits such as aquantum processor with controllable programmable qubit parameters.

FIG. 4 shows a logical qubit 400 comprising three hybrid qubits (forexample, hybrid qubit 470; only hybrid qubit 470 is called out in FIG. 4to reduce clutter) and two tunable ZZ-couplers 411, 412 couplinginformation therebetween. While logical qubit 400 shown in FIG. 4includes three hybrid qubits 470 and two couplers 411, 412, those ofskill in the art will appreciate that logical qubit 400 may include anynumber of hybrid qubits, and any number of coupling devices couplinginformation therebetween (for example, 2 hybrid qubits and 1 couplingdevice, 5 hybrid qubits and 4 coupling devices, etc.).

Each hybrid qubit 470 of logical qubit 400 may be substantially similarto hybrid qubit 300 from FIG. 3. For example, hybrid qubit 470 comprisesa first qubit 401 (i.e., similar to first qubit 301 from FIG. 3) and asecond qubit 451 (i.e., similar to second or adjustment or orthogonalcontrol qubit 351 from FIG. 3) galvanically coupled to first qubit 401.Second qubit 451 is galvanically coupled to first qubit 401 to, forexample, achieve a strong interaction between qubits 451 and 401.However, second qubit 451 and first qubit 401 may not be galvanicallycoupled in alternative embodiments as long as second qubit 451 isstrongly coupled to first qubit 401 by communicative coupling means,such as via inductive coupling. In other words, first qubit 401 andsecond qubit 451 may be strongly coupled such that the orientation offirst qubit 401 and second qubit 451 may always be similar to each other(either 1 or 0) and therefore one qubit may not have a bit flip thatopposes the orientation of the other qubit. Logical qubit 400 maycomprise an effective tunneling amplitude which may be derived from theeffective tunneling amplitudes of the individual hybrid qubits 470 oflogical qubit 400 and effective persistent current which may, forexample, be derived from the effective persistent currents of theindividual hybrid qubits 470 of logical qubit 400.

Communicatively coupling additional hybrid qubits to logical qubit 400increases the effective length of logical qubit 400. Increasing theeffective length of the logical qubits (by, for example, forming logicalqubits with four or more individual qubits) increases the effectiveconnectivity of the logical qubits in a quantum processor. Thisadvantageously allows for more flexibility in embedding a problem intothe quantum processor. Each hybrid qubit 470 in logical qubit 400comprises an effective tunneling amplitude. For example, hybrid qubit470 of logical qubit 400 comprises an effective tunneling amplitudewhich may depend on the tunneling amplitude of first qubit 401 andsecond qubit 451 galvanically coupled to first qubit 401.

Some problems may benefit from having communicatively coupled qubits ina logical qubit with an effective h parameter distributed among thecommunicatively coupled qubits in order to achieve better precision.This results in multiple qubits within a chain having non-zeroindividual h parameters which limits the number of qubits with freelyadjustable parameters such as tunneling amplitude. Using hybrid qubitson the other hand may allow for controllably adjusting a tunnelingamplitude within a logical qubit (and thereby adjusting the effectivetunneling amplitude of the logical qubit) without affecting a persistentcurrent within the logical qubit such that the h and J of the hybridqubit may not be affected. Similar to hybrid qubit 300 of FIG. 3, byadjusting the tunneling amplitude of second qubit 451, the effectivetunneling amplitude of hybrid qubit 470 may be adjusted or maintained.The tunneling amplitude of second qubit 451 may be adjusted by a fluxsignal coupled into compound Josephson junction 461 of second qubit 451via programming subsystem 441. When the tunneling amplitude of secondqubit 451 is adjusted so that the tunneling amplitude of second qubit451 is very large compared to the tunneling amplitude of first qubit401, the effective tunneling amplitude of hybrid qubit 470 may not besubstantially affected by the tunneling amplitude of first qubit 401.Hence, the persistent current of first qubit 401 may also not beaffected by a change in the tunneling amplitude of second qubit 451.Therefore, by only adjusting the tunneling amplitude of second qubit451, the effective tunneling amplitude of hybrid qubit 470 may beadjusted without affecting the persistent current of first qubit 401which achieves orthogonal control of otherwise non-orthogonal qubitparameters such as tunneling amplitude and persistent current. Likewise,by controllably adjusting the effective tunneling amplitude of any orall of the hybrid qubits of a logical qubit, the effective tunnelingamplitude of the logical qubit may be maintained so that the logicalqubit may continue to operate in the quantum regime despite theinclusion of multiple hybrid qubits within logical qubit 400 and thenormal quantum annealing process may be unaffected.

FIG. 5 shows a method 500 for achieving orthogonal control of at leasttwo non-orthogonal qubit parameters in a quantum processor comprising aplurality of hybrid qubits. Method 500 includes three acts 501-503,though those of skill in the art will appreciate that in alternativeembodiments certain acts may be omitted and/or additional acts may beadded. Those of skill in the art will appreciate that the illustratedorder of the acts is shown for exemplary purposes only and may change inalternative embodiments.

At 501, a first hybrid qubit is formed by galvanically coupling a firstqubit and a second qubit together. The first hybrid qubit may have aneffective first programmable parameter and an effective secondprogrammable parameter. The effective first programmable parameter may,for example, depend on a first programmable parameter of the first qubitand a first programmable parameter of the second qubit, while theeffective second programmable parameter may, for example, depend on asecond programmable parameter of the first qubit. As described in FIG.4, the effective first programmable parameter may be an effectivetunneling amplitude of the first hybrid qubit while the effective secondprogrammable parameter may be an effective persistent current of thefirst hybrid qubit. Similarly, the first programmable parameter of thefirst qubit in the first hybrid qubit may be a tunneling amplitude, thefirst programmable parameter of the second qubit in the first hybridqubit may be a tunneling amplitude, and the second programmableparameter of the first qubit in the first hybrid qubit may be apersistent current.

At 502, a second hybrid qubit is communicatively coupled to the firsthybrid qubit via a first coupling device such that the first hybridqubit, the second hybrid qubit and the first coupling device behave as asingle logical qubit having an effective first programmable parameterand an effective second programmable parameter where the effective firstprogrammable parameter may be an effective tunneling amplitude and theeffective second programmable parameter may be an effective persistentcurrent. While the logical qubit described in FIG. 5 comprises 2 hybridqubits, a logical qubit may comprise any number of communicativelycoupled hybrid qubits. For example, a logical qubit may comprise 1hybrid qubit, 3 hybrid qubits, 8 hybrid qubits and so on. The effectivetunneling amplitude of the logical qubit depends on the effectivetunneling amplitudes of the first hybrid qubit and the second hybridqubit. Therefore, adjusting the effective tunneling amplitude of thefirst and/or the second hybrid qubit may affect the effective tunnelingamplitude of the logical qubit.

At 503, the effective first programmable parameter (e.g., the effectivetunneling amplitude) of the logical qubit is programmed via theprogramming subsystem. The effective tunneling amplitude of the logicalqubit may be programmed by programming the respective effectivetunneling amplitudes of any or all of the hybrid qubits comprised in thelogical qubit (i.e., the first hybrid qubit and/or the second hybridqubit). For example, the effective tunneling amplitude of logical qubit400 as shown in FIG. 4 may be programmed by tuning the effectivetunneling amplitude of any or all of the hybrid qubits such as hybridqubit 470. Tuning the effective tunneling amplitude of a hybrid qubitwas described earlier in FIG. 3.

FIG. 6 shows a general method 600 for achieving orthogonal control of atleast two non-orthogonal qubit parameters in a quantum processor. Method600 includes three acts 601-603, though those of skill in the art willappreciate that in alternative embodiments certain acts may be omittedand/or additional acts may be added. Those of skill in the art willappreciate that the illustrated order of the acts is shown for exemplarypurposes only and may change in alternative embodiments.

At 601, a first qubit and a second qubit are communicatively coupledsuch that the first qubit and the second qubit together behave as asingle logical qubit having an effective first programmable parameterand an effective second programmable parameter. A logical qubit maycomprise a first qubit and a second qubit as shown in FIG. 1 (e.g.,qubits 101 and 102) or as shown in FIG. 3 (e.g., first qubit 301 andsecond or adjustment or orthogonal control qubit 351). The effectivefirst and second programmable parameters of the logical qubit may be aneffective tunneling amplitude and an effective persistent current,respectively. The first qubit and the second qubit may becommunicatively coupled together via a coupling device such as couplingdevice 111 of FIG. 1 coupling qubits 101 and 102 together.Communicatively coupling the first and the second qubit may includeferromagnetically, anti-ferromagnetically, and/or transversely couplingthe first and the second qubit. In alternative embodiments, the firstqubit and the second qubit may be galvanically coupled as shown in FIG.3 where first qubit 301 is galvanically coupled to second or adjustmentor orthogonal control qubit 351 at Josephson junction 341.

At 602, effective first programmable parameter (i.e., effectivetunneling amplitude) of the logical qubit is programmed via aprogramming subsystem without affecting the effective secondprogrammable parameter (i.e., effective persistent current) of thelogical qubit. The first qubit may have a first programmable parameterand a second programmable parameter. The second qubit may have at leasta first programmable parameter. The first programmable parameter of thefirst qubit may be a tunneling amplitude of the first qubit, the secondprogrammable parameter of the first qubit may be a persistent current ofthe first qubit, and the first programmable parameter of the secondqubit may be a tunneling amplitude of the second qubit. The effectivetunneling amplitude of the logical qubit may be programmed by adjustingthe tunneling amplitude of the first qubit and/or the tunnelingamplitude of the second qubit via the programming subsystem (forexample, programming subsystem 121 and/or 123 of FIG. 1 and programmingsubsystem 323 of FIG. 3). As illustrated and described previously inreference to FIGS. 1 and 3, programming the effective tunnelingamplitude of a logical qubit may not affect the effective persistentcurrent of the logical qubit.

At 603, the effective second programmable parameter (i.e., effectivepersistent current) of the logical qubit is programmed via theprogramming subsystem. The effective persistent current of the logicalqubit may, at least in part depend on the persistent current of thefirst qubit without restricting the persistent current of the secondqubit. The effective persistent current of the logical qubit may beprogrammed by adjusting the persistent current of the first qubit and/orthe persistent current of the second qubit. A programming subsystem maybe used to adjust the persistent current of the first and/or secondqubit which ultimately adjusts the effective persistent current of thelogical qubit. For example, programming subsystems 122 and 124 of FIG. 1as well as programming subsystem 322 of FIG. 3 may each be used toadjust the persistent current of respective qubits 101, 102 of FIG. 1and respective first qubit 301 of FIG. 3. The tunable persistent currentof qubits 101 and 102 of FIG. 1 defines the effective persistent currentof the logical qubit comprising qubits 101 and 102. The tunnelingamplitude of, for example, the second qubit of the logical qubit may notaffect the persistent current of the first qubit of the logical qubit.For example, as described in FIG. 3, adjusting the tunneling amplitudeof second or adjustment or orthogonal control qubit 351 may affect theeffective tunneling amplitude of hybrid qubit 300 (i.e., the logicalqubit). However, as previously described, the change in effectivetunneling amplitude of the logical qubit may not substantially affectthe effective persistent current of the logical qubit which achievesorthogonal control of otherwise non-orthogonal qubit parameters.

Method 600 may be used to achieve orthogonal control of non-orthogonalparameters of a hybrid qubit or a plurality of communicatively coupledqubits behaving as a single logical qubit. As such, method 600 may beused with logical qubits comprising qubit loops communicatively coupledvia coupling devices (for example, logical qubit 100 of FIG. 1comprising qubits 101, 102, 103 and coupling devices 111, 112) as wellas with a hybrid qubit comprising a first qubitcommunicatively/galvanically coupled to a second qubit (for example,hybrid qubit 300 of FIG. 3 comprising first qubit 301 and second oradjustment or orthogonal control qubit 351). A logical qubit maycomprise a single hybrid qubit such as hybrid qubit 300 of FIG. 3. Alogical qubit may also comprise a plurality of communicatively coupledhybrid qubits such as logical qubit 400 of FIG. 4.

Although it may be desirable to form a hybrid qubit comprising a firstqubit galvanically coupled to a second qubit, galvanic coupling ofqubits is not necessary. As such, in alternative embodiments, a firstqubit may be communicatively coupled to a second qubit via non-galvanicmeans such that the two communicatively coupled qubits may behave as ahybrid qubit. The coupling established between the two qubits may beinductive. As long as the first qubit and the second qubit are stronglycoupled to each other, the type of coupling established between the twoqubits (e.g., galvanic or inductive) does not matter. In other words,the first qubit and the second qubit may be strongly coupled such thatthe orientation of the first qubit and the second qubit may always besimilar to each other (either 1 or 0) and therefore one qubit may nothave a bit flip that opposes the orientation of the other qubit. Thesecond qubit of the hybrid qubit may comprise a compound Josephsonjunction that may be programmed via a programming subsystem to provide atunable tunneling amplitude. In alternative embodiments, the compoundJosephson junction of the second qubit may be replaced with a singleJosephson junction in parallel connection with a tunable capacitor.However, adding a capacitor to replace the compound Josephson junctionmay add unwanted noise to the hybrid qubit and therefore may requireadditional structure(s) to shield and/or reduce noise generated from thetunable capacitor. Therefore, the second qubit of the hybrid qubit maycomprise a compound Josephson junction to adjust the tunnelingamplitude, a large Josephson junction to galvanically couple the firstqubit to the second qubit and at least one additional Josephsonjunction. The at least one additional Josephson junction of the secondqubit generates the necessary inductance needed to strongly couple thesecond qubit to the first qubit of the hybrid qubit. Without the atleast one additional Josephson junction, the structure of the secondqubit may need to be larger in size (i.e., the qubit loop length of thesecond qubit may need to be increased) in order to achieve the necessaryinductance. Therefore, forming at least one additional Josephsonjunction in the second qubit of the hybrid qubit reduces the size of thesecond qubit.

Throughout this specification and the appended claims, the term“superconducting” when used to describe a physical structure such as a“loop of superconducting material” is used to indicate a material thatis capable of behaving as a superconductor at an appropriatetemperature. A superconducting material may not necessarily be acting asa superconductor at all times in all embodiments of the present systemsand methods.

A programmable parameter of a qubit may be a parameter that can beadjusted in order to solve a problem using a quantum processor. Examplesof programmable parameters include: tunneling amplitude, persistentcurrent, spin (h), coupling strength (J), etc. Some programmableparameters may have a direct or indirect effect on other programmableparameters. Achieving orthogonal control of such non-orthogonalparameters is a challenge that is addressed in the present systems andmethods by the use of logical qubits and/or hybrid qubits.

Programmable parameters of a qubit may be programmed using a dedicatedprogramming subsystem. For example, as shown in FIG. 1, a firstprogrammable parameter such as the tunneling amplitude of qubit 101 maybe adjusted by programming the respective programming subsystem 121 anda second programmable parameter such as the persistent current of qubit101 may be adjusted by programming the respective programming subsystem122. A programming subsystem may be realized, for example, by aninductive coupling structure to a programming system. Such a programmingsystem may be separate from the quantum processor, or it may be includedlocally (i.e., on-chip with the quantum processor) as described in U.S.Pat. Nos. 7,876,248 and 8,035,540.

A qubit may be communicatively coupled to another qubit via a couplingdevice so that the two qubits and the coupling device collectivelybehave as a single logical qubit. A logical qubit may also be a singlehybrid qubit. Further still, a logical qubit may be formed bycommunicatively coupling a hybrid qubit and another hybrid qubit via acoupling device. A logical qubit may therefore have any number ofqubits/hybrid qubits (for example, 2 qubits/hybrid qubits, 5qubits/hybrid qubits, 9 qubits/hybrid qubits, etc.) A pair ofqubits/hybrid qubits in a logical qubit may be communicatively coupledvia a coupling device. A logical qubit comprising two or morequbits/hybrid qubits may improve the effective connectivity of a quantumprocessor comprising a plurality of qubits. This improved effectiveconnectivity gives more flexibility in embedding problems (i.e.,assigning variables in a problem to qubits) into the quantum processorand may speed up processing time.

A qubit/hybrid qubit may be communicatively coupled to anotherqubit/hybrid qubit via a coupling device to form a logical qubit.Throughout this specification and the appended claims, the terms“communicative” or “communicatively” when used to describe couplingbetween two qubits or hybrid qubits is used to describe any form ofcoupling information between qubits (including but not limited toferromagnetic coupling, anti-ferromagnetic coupling, and transversecoupling) such that the pair of coupled qubits or hybrid qubits may bein communication with each other.

A hybrid qubit may comprise a first qubit galvanically coupled to asecond qubit. However, in alternate embodiments, the first qubit of ahybrid qubit may be strongly inductively coupled to the second qubit ofthe hybrid qubit. Throughout this specification and the appended claims,the terms “strong” or “strongly” when used to describe the couplingstrength established between the two qubits of a hybrid qubit describesthe first qubit of a hybrid qubit that is communicatively coupled to thesecond qubit of a hybrid qubit such that the orientation of the firstqubit and the second qubit of the hybrid qubit may remain similar toeach other and the coupling strength established between the pair ofqubits may be strong enough to prevent one qubit from flipping withrespect to the other qubit of the hybrid qubit. In other words, both thefirst qubit and the second qubit of the hybrid qubit may representeither a logical ‘1’ or logical ‘0’.

A logical qubit may at least comprise an effective first programmableparameter and an effective second programmable parameter. Such effectiveprogrammable parameters may depend on the individual programmableparameters of the qubits that make up a logical qubit. For example, theeffective first programmable parameter of a logical qubit may be aneffective tunneling amplitude of the logical qubit which may depend onthe individual tunneling amplitudes of the qubits that make up thelogical qubit. In other words, adjusting the tunneling amplitude of aqubit in a logical qubit may impact the overall (i.e., effective)tunneling amplitude of the logical qubit. Therefore, throughout thisspecification and the appended claims, the term “effective” when used todescribe a programmable parameter, describes the overallvalue/characteristic of the programmable parameter that influences ordefines the behavior of a logical qubit and is the result of acombination of similar individual programmable parameters that make upthe effective programmable parameter. Similarly, throughout thisspecification and the appended claims, the term “effective” when used todescribe a connectivity of a logical qubit (i.e., effectiveconnectivity), describes the maximum number of possible communicativecoupling paths that are physically available (e.g., whether active ornot) to communicably couple between logical qubits and individual qubitsin a quantum processor with the use of intervening qubits comprised inthe logical qubit.

FIG. 7 illustrates computing system 700 including a digital computer 705coupled to an analog computer 751. In some embodiments the analogcomputer 751 is a quantum computer and the digital computer 705 is aclassical computer. The exemplary digital computer 705 includes adigital processor that may be used to perform classical digitalprocessing tasks described in the present systems and methods. Thoseskilled in the relevant art will appreciate that the present systems andmethods can be practiced with other digital computer configurations,including hand-held devices, multiprocessor systems,microprocessor-based or programmable consumer electronics, personalcomputers (“PCs”), network PCs, mini-computers, mainframe computers, andthe like, when properly configured or programmed to form special purposemachines, and/or when communicatively coupled to control an analogcomputer, for instance a quantum computer.

Digital computer 705 will at times be referred to in the singularherein, but this is not intended to limit the application to a singledigital computer. The present systems and methods can also be practicedin distributed computing environments, where tasks or sets ofinstructions are performed or executed by remote processing devices,which are linked through a communications network. In a distributedcomputing environment sets of instruction, sometimes known as programmodules, may be located in both local and remote memory storage devices.

Digital computer 705 may include at least one digital processor (suchas, central processor unit 710), at least one system memory 720, and atleast one system bus 717 that couples various system components,including system memory 720 to central processor unit 710.

The digital processor may be any logic processing unit, such as one ormore central processing units (“CPUs”), graphics processing units(“GPUs”), digital signal processors (“DSPs”), application-specificintegrated circuits (“ASICs”), field-programmable gate arrays (“FPGAs”),etc. Unless described otherwise, the construction and operation of thevarious blocks shown in FIG. 7 are of conventional design. As a result,such blocks need not be described in further detail herein, as they willbe understood by those skilled in the relevant art.

Digital computer 705 may include a user input/output subsystem 711. Insome embodiments, the user input/output subsystem includes one or moreuser input/output components such as a display 712, mouse 713, and/orkeyboard 714. System bus 717 can employ any known bus structures orarchitectures, including a memory bus with a memory controller, aperipheral bus, and a local bus. System memory 720 may includenon-volatile memory, such as read-only memory (“ROM”), static randomaccess memory (“SRAM”), Flash NAND; and volatile memory such as randomaccess memory (“RAM”) (not shown). An basic input/output system (“BIOS”)721, which can form part of the ROM, contains basic routines that helptransfer information between elements within digital computer 705, suchas during startup.

Digital computer 705 may also include other non-volatile memory 715.Non-volatile memory 715 may take a variety of forms, including: a harddisk drive for reading from and writing to a hard disk, an optical diskdrive for reading from and writing to removable optical disks, and/or amagnetic disk drive for reading from and writing to magnetic disks. Theoptical disk can be a CD-ROM or DVD, while the magnetic disk can be amagnetic floppy disk or diskette. Non-volatile memory 715 maycommunicate with digital processor via system bus 717 and may includeappropriate interfaces or controllers 716 coupled to system bus 717.Non-volatile memory 715 may serve as long-term storage forcomputer-readable instructions, data structures, sets of processorreadable instruction (also called program modules) and other data fordigital computer 705.

Although digital computer 705 has been described as employing harddisks, optical disks and/or magnetic disks, those skilled in therelevant art will appreciate that other types of non-volatilecomputer-readable media may be employed, such a magnetic cassettes,flash memory cards, Flash, ROMs, smart cards, etc. Those skilled in therelevant art will appreciate that some computer architectures conflatevolatile memory and non-volatile memory. For example, data in volatilememory can be cached to non-volatile memory. Or a solid-state disk thatemploys integrated circuits to provide non-volatile memory. Somecomputers place data traditionally stored on disk in memory. As well,some media that is traditionally regarded as volatile can have anon-volatile form, e.g., Non-Volatile Dual In-line Memory Modulevariation of Dual In Line Memory Modules.

Various sets of computer- or processor-readable instructions,application programs and/or data can be stored in system memory 720. Forexample, system memory 720 may store an operating system 723, and a setof computer- or processor-readable server instructions 727. In someembodiments, the set of server instructions 727 includes instruction forcommunicating with remote clients and scheduling use of resourcesincluding resources on the digital computer 705 and analog computer 751.For example, a Web server application and/or Web client or browserapplication for permitting digital computer 705 to exchange data withsources via the Internet, corporate Intranets, or other networks, aswell as with other server applications executing on server computers.

In some embodiments system memory 720 may store a set of computer- orprocessor-readable calculation instructions 731 to performpre-processing, co-processing, and post-processing to analog computer751. In accordance with the present systems and methods, system memory720 may store at set of analog computer interface instructions 735operable to interact with the analog computer 751.

In some embodiments system memory 720 may store a set of non-orthogonalqubits instructions 739. For example, the set of non-orthogonal qubitsinstructions 739 can implement the methods like those described in FIG.6 on digital computer 705 and analog computer 751. In some examples, theset of non-orthogonal qubits instructions 739 can be used to controlnon-orthogonal qubit parameters. In some examples of the presentinvention, the set of non-orthogonal qubits instructions 739 can be usedto implement the methods shown in FIGS. 2, 5 and 6.

While shown in FIG. 7 as being stored in system memory 720, the sets ofinstructions shown and other data can also be stored elsewhere includingin nonvolatile memory 715.

The analog computer 751 is provided in an isolated environment (notshown). For example, where the analog computer 751 is a quantumcomputer, the environment shields the internal elements of the quantumcomputer from heat, magnetic field, and the like. The analog computer751 includes an analog processor 740. Examples of an analog processorinclude quantum processors such as the portions of those shown in FIGS.1, 3 and 4.

A quantum processor includes programmable elements such as qubits,couplers, and other devices. The qubits are readout via readout outsystem 760. These results are fed to the various sets of computer orprocessor readable instructions for the digital computer 705 includingthe set of server instructions 727, the set of calculation instructions731, the set of analog computer interface instructions 735, or othersets of instructions stored in nonvolatile memory 715, returned over anetwork or the like. The qubits include those shown in FIGS. 1, 3 and 4and include hybrid qubits, such as, qubit 300 and qubit 470. The qubitsare controlled via qubit control system 765. The qubit control system765 includes programming subsystems, such as, programming subsystems121, 123, and 125. The couplers are controlled via coupler controlsystem 770. The coupler control system 770 includes programmingsubsystems, such as, programming subsystems 141 and 142. In someexamples of the qubit control system 765 and the coupler control system770 are used to control couplers like couplers 111, 112, 411 and 412 asdescribed herein on analog processor 740.

In some examples the digital computer 705 can operate in a networkingenvironment using logical connections to at least one client computersystem. In some examples the digital computer 705 is coupled via logicalconnections to at least one database system. These logical connectionsmay be formed using any means of digital communication, for example,through a network, such as a local area network (“LAN”) or a wide areanetwork (“WAN”) including, for example, the Internet. The networkingenvironment may include wired or wireless enterprise-wide computernetworks, intranets, extranets, and/or the Internet. Other examples mayinclude other types of communication networks such as telecommunicationsnetworks, cellular networks, paging networks, and other mobile networks.The information sent or received via the logical connections may or maynot be encrypted. When used in a LAN networking environment, digitalcomputer 705 may be connected to the LAN through an adapter or networkinterface card (“NIC”) (communicatively linked to system bus 717). Whenused in a WAN networking environment, digital computer 105 may includean interface and modem (not shown), or a device such as NIC, forestablishing communications over the WAN. Non-networked communicationsmay additionally, or alternatively be employed.

Throughout this specification and the appended claims, the term“ferromagnetic region” when used to describe for example thesusceptibility of a coupling device is used to describe a range of fluxbiases that may be applied to a coupling device such that a pair ofsuperconducting devices communicatively coupled by the coupling deviceis ferromagnetically coupled. Similarly, throughout this specificationand the appended claims, the term “anti-ferromagnetic region” when usedto describe for example the susceptibility of a coupling device is usedto describe a range of flux biases that may be applied to a couplingdevice such that a pair of superconducting devices communicativelycoupled by the coupling device is anti-ferromagnetically coupled.

Throughout this specification and the appended claims, the terms“coupler” and “coupling device” are used interchangeably. However, both“coupler” and “coupling device” are used to describe a coupling loop ofsuperconducting material interrupted by at least one Josephson junctionthat may be used to ferromagnetically, or anti-ferromagnetically couplea pair of superconducting devices together. Furthermore, throughout thisspecification and the appended claims, the phrase “a pair ofcommunicatively coupled superconducting devices” is used to describe apair of superconducting devices that may be ferromagnetically, oranti-ferromagnetically coupled together by a coupling device.

Throughout this specification and the appended claims, the term“superconducting” when used to describe a physical structure such as a“loop of superconducting material” is used to indicate a material thatis capable of behaving as a superconductor at an appropriatetemperature. A superconducting material may not necessarily be acting asa superconductor at all times in all embodiments of the present systemsand methods.

The above description of illustrated embodiments, including what isdescribed in the Abstract, is not intended to be exhaustive or to limitthe embodiments to the precise forms disclosed. Although specificembodiments of and examples are described herein for illustrativepurposes, various equivalent modifications can be made without departingfrom the spirit and scope of the disclosure, as will be recognized bythose skilled in the relevant art. The teachings provided herein of thevarious embodiments can be applied to other systems and methods ofsuperconducting circuits, not necessarily the exemplary methods forquantum computation generally described above.

The various embodiments described above can be combined to providefurther embodiments. All of the U.S. patents, U.S. patent applicationpublications, U.S. patent applications, International (PCT) patentapplications referred to in this specification and/or listed in theApplication Data Sheet including U.S. provisional patent applicationSer. No. 61/857,601 filed Jul. 23, 2013, are incorporated herein byreference, in their entirety. Aspects of the embodiments can bemodified, if necessary, to employ systems, circuits and concepts of thevarious patents, applications and publications to provide yet furtherembodiments. These and other changes can be made to the embodiments inlight of the above-detailed description. In general, in the followingclaims, the terms used should not be construed to limit the claims tothe specific embodiments disclosed in the specification and the claims,but should be construed to include all possible embodiments along withthe full scope of equivalents to which such claims are entitled.Accordingly, the claims are not limited by the disclosure.

The invention claimed is:
 1. A method of controlling qubit parameters ina quantum processor, wherein the quantum processor includes a pluralityof qubits, each qubit having a respective first programmable parameterand a respective second programmable parameter that at least partiallydepends on the respective first programmable parameter, and a pluralityof coupling devices that each selectively provide communicative couplingbetween respective pairs of the qubits, the method comprising:communicatively coupling at least three of the qubits to one another asa single logical qubit, the single logical qubit formed by a firstoutermost qubit, a second outermost qubit and at least one intermediaryqubit, the at least one intermediary qubit communicatively coupledbetween the first and the second outermost qubits with couplingmagnitudes that are greater than each respective qubit tunnelingamplitude, the first outermost qubit being an outermost qubit of thequbits of the logical qubit in a first direction along a logical qubitpath defined by the qubits of the logical qubit and the second outermostqubit being an outermost qubit in a second direction along the logicalqubit path; programming the first and the second outermost qubits tohave respective first programmable parameters less than or equal to afirst value; and programming the at least one intermediary qubit to havea spin of level zero and to have respective values of the firstprogrammable parameter higher than the first value; wherein: the firstprogrammable parameter is tunneling amplitude, and programming the firstprogrammable parameter of the first and the second outermost qubitsincludes programming a respective tunneling amplitude of the first andthe second outermost qubits via a programming subsystem; and the secondprogrammable parameter is a persistent current of the second qubit, andwherein programming the respective tunneling amplitude of the at leastone intermediary qubit includes programming a respective tunnelingamplitude of the at least one intermediary qubit via the programmingsubsystem without affecting the persistent current of the first and thesecond outermost qubits.
 2. The method of claim 1 wherein:communicatively coupling at least three of the qubits to one another asa single logical qubit includes communicatively coupling at least twoqubits as respective intermediary qubits communicatively coupled betweenthe first and the second outermost qubits; and programming the at leastone intermediary qubit to have a spin of level zero and to haverespective values of the first programmable parameter higher than thefirst value includes programming all of the intermediary qubits to havea spin of level zero and to have respective values of the firstprogrammable parameter higher than the first value.
 3. A quantumprocessor apparatus, comprising: a plurality of qubits, each qubithaving a respective first programmable parameter and a respective secondprogrammable parameter that at least partially depends on the respectivefirst programmable parameter; and a plurality of coupling devices thateach selectively provide communicative coupling between respective pairsof the plurality of qubits; wherein: at least three of the plurality ofqubits are communicatively coupled to one another as a single logicalqubit, the single logical qubit formed by a first outermost qubit, asecond outermost qubit and at least one intermediary qubit, the at leastone intermediary qubit communicatively coupled between the firstoutermost qubit and the second outermost qubit with coupling magnitudesthat are greater than each respective qubit tunneling amplitude, thefirst outermost qubit being an outermost qubit of the qubits of thelogical qubit in a first direction along a logical qubit path defined bythe qubits of the logical qubit and the second outermost qubit being anoutermost qubit in a second direction along the logical qubit path; thefirst outermost qubit and the second outermost qubit have respectivefirst programmable parameters less than or equal to a first value; theat least one of the at least three of the plurality of qubits has a spinof level zero and respective values of the first programmable parameterhigher than the first value; the first programmable parameter istunneling amplitude, and a respective tunneling amplitude of the firstand the second outermost qubits is less than or equal to the firstvalue; and the second programmable parameter is a persistent current ofthe second outermost qubit, and a respective tunneling amplitude of theat least one intermediary qubit does not affect the persistent currentof the first outermost qubit and the second outermost qubit.
 4. Thequantum processor apparatus of claim 3 wherein: the single logical qubitincludes at least two qubits as respective intermediary qubitscommunicatively coupled between the first outermost qubit and the secondoutermost qubit, and all of the intermediary qubits have a spin of levelzero and have respective values of the first programmable parameterhigher than the first value.
 5. The quantum processor apparatus of claim3, further comprising: at least one first programming subsystemcommunicatively coupleable to a compound Josephson junction of at leastone of the qubits and operable to program a tunneling amplitude of theat least one of the qubits; and at least one second programmingsubsystem communicatively coupleable to a qubit loop of at least one ofthe qubits and operable to program a persistent current of the at leastone of the qubits.